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 $eval_func_interface=generate('    function_options & eval_func(eval_funcp_${N} e);'."\n",'','','');
  66
  67 $evalf_func_interface=generate('    function_options & evalf_func(evalf_funcp_${N} ef);'."\n",'','','');
  68
  69 $derivative_func_interface=generate('    function_options & derivative_func(derivative_funcp_${N} d);'."\n",'','','');
  70
  71 $series_func_interface=generate('    function_options & series_func(series_funcp_${N} s);'."\n",'','','');
  72
  73 $constructors_interface=generate(
  74 '    function(unsigned ser, ${SEQ1});'."\n",
  75 'const ex & param${N}','','');
  76
  77 $constructors_implementation=generate(
  78         <<'END_OF_CONSTRUCTORS_IMPLEMENTATION','const ex & param${N}','param${N}','');
  79 function::function(unsigned ser, ${SEQ1})
  80         : exprseq(${SEQ2}), serial(ser)
  81 {
  82         tinfo_key = TINFO_function;
  83 }
  84 END_OF_CONSTRUCTORS_IMPLEMENTATION
  85
  86 $eval_switch_statement=generate(
  87         <<'END_OF_EVAL_SWITCH_STATEMENT','seq[${N}-1]','','');
  88         case ${N}:
  89                 eval_result = ((eval_funcp_${N})(registered_functions()[serial].eval_f))(${SEQ1});
  90                 break;
  91 END_OF_EVAL_SWITCH_STATEMENT
  92
  93 $evalf_switch_statement=generate(
  94         <<'END_OF_EVALF_SWITCH_STATEMENT','eseq[${N}-1]','','');
  95         case ${N}:
  96                 return ((evalf_funcp_${N})(registered_functions()[serial].evalf_f))(${SEQ1});
  97 END_OF_EVALF_SWITCH_STATEMENT
  98
  99 $diff_switch_statement=generate(
 100         <<'END_OF_DIFF_SWITCH_STATEMENT','seq[${N}-1]','','');
 101         case ${N}:
 102                 return ((derivative_funcp_${N})(registered_functions()[serial].derivative_f))(${SEQ1},diff_param);
 103 END_OF_DIFF_SWITCH_STATEMENT
 104
 105 $series_switch_statement=generate(
 106         <<'END_OF_SERIES_SWITCH_STATEMENT','seq[${N}-1]','','');
 107         case ${N}:
 108                 try {
 109                         res = ((series_funcp_${N})(registered_functions()[serial].series_f))(${SEQ1},r,order,options);
 110                 } catch (do_taylor) {
 111                         res = basic::series(r, order, options);
 112                 }
 113                 return res;
 114 END_OF_SERIES_SWITCH_STATEMENT
 115
 116 $eval_func_implementation=generate(
 117         <<'END_OF_EVAL_FUNC_IMPLEMENTATION','','','');
 118 function_options & function_options::eval_func(eval_funcp_${N} e)
 119 {
 120         test_and_set_nparams(${N});
 121         eval_f = eval_funcp(e);
 122         return *this;
 123 }
 124 END_OF_EVAL_FUNC_IMPLEMENTATION
 125
 126 $evalf_func_implementation=generate(
 127         <<'END_OF_EVALF_FUNC_IMPLEMENTATION','','','');
 128 function_options & function_options::evalf_func(evalf_funcp_${N} ef)
 129 {
 130         test_and_set_nparams(${N});
 131         evalf_f = evalf_funcp(ef);
 132         return *this;
 133 }
 134 END_OF_EVALF_FUNC_IMPLEMENTATION
 135
 136 $derivative_func_implementation=generate(
 137         <<'END_OF_DERIVATIVE_FUNC_IMPLEMENTATION','','','');
 138 function_options & function_options::derivative_func(derivative_funcp_${N} d)
 139 {
 140         test_and_set_nparams(${N});
 141         derivative_f = derivative_funcp(d);
 142         return *this;
 143 }
 144 END_OF_DERIVATIVE_FUNC_IMPLEMENTATION
 145
 146 $series_func_implementation=generate(
 147         <<'END_OF_SERIES_FUNC_IMPLEMENTATION','','','');
 148 function_options & function_options::series_func(series_funcp_${N} s)
 149 {
 150         test_and_set_nparams(${N});
 151         series_f = series_funcp(s);
 152         return *this;
 153 }
 154 END_OF_SERIES_FUNC_IMPLEMENTATION
 155
 156 $interface=<<END_OF_INTERFACE;
 157 /** \@file function.h
 158  *
 159  *  Interface to class of symbolic functions. */
 160
 161 /*
 162  *  This file was generated automatically by function.pl.
 163  *  Please do not modify it directly, edit the perl script instead!
 164  *  function.pl options: \$maxargs=${maxargs}
 165  *
 166  *  GiNaC Copyright (C) 1999-2003 Johannes Gutenberg University Mainz, Germany
 167  *
 168  *  This program is free software; you can redistribute it and/or modify
 169  *  it under the terms of the GNU General Public License as published by
 170  *  the Free Software Foundation; either version 2 of the License, or
 171  *  (at your option) any later version.
 172  *
 173  *  This program is distributed in the hope that it will be useful,
 174  *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 175  *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 176  *  GNU General Public License for more details.
 177  *
 178  *  You should have received a copy of the GNU General Public License
 179  *  along with this program; if not, write to the Free Software
 180  *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 181  */
 182
 183 #ifndef __GINAC_FUNCTION_H__
 184 #define __GINAC_FUNCTION_H__
 185
 186 #include <string>
 187 #include <vector>
 188
 189 // CINT needs <algorithm> to work properly with <vector>
 190 #include <algorithm>
 191
 192 #include "exprseq.h"
 193
 194 // the following lines have been generated for max. ${maxargs} parameters
 195 $declare_function_macro
 196 // end of generated lines
 197
 198 #define REGISTER_FUNCTION(NAME,OPT) \\
 199 unsigned NAME##_SERIAL::serial = \\
 200         GiNaC::function::register_new(GiNaC::function_options(#NAME).OPT);
 201
 202 namespace GiNaC {
 203
 204 class function;
 205 class symmetry;
 206
 207 typedef ex (* eval_funcp)();
 208 typedef ex (* evalf_funcp)();
 209 typedef ex (* derivative_funcp)();
 210 typedef ex (* series_funcp)();
 211
 212 // the following lines have been generated for max. ${maxargs} parameters
 213 $typedef_eval_funcp
 214 $typedef_evalf_funcp
 215 $typedef_derivative_funcp
 216 $typedef_series_funcp
 217 // end of generated lines
 218
 219 // Alternatively, an exvector may be passed into the static function, instead
 220 // of individual ex objects.  Then, the number of arguments is not limited.
 221 typedef ex (* eval_funcp_exvector)(const exvector &);
 222 typedef ex (* evalf_funcp_exvector)(const exvector &);
 223 typedef ex (* derivative_funcp_exvector)(const exvector &, unsigned);
 224 typedef ex (* series_funcp_exvector)(const exvector &, const relational &, int, unsigned);
 225
 226
 227 class function_options
 228 {
 229         friend class function;
 230         friend class fderivative;
 231 public:
 232         function_options();
 233         function_options(std::string const & n, std::string const & tn=std::string());
 234         ~function_options();
 235         void initialize();
 236         function_options & set_name(std::string const & n, std::string const & tn=std::string());
 237         function_options & latex_name(std::string const & tn);
 238 // the following lines have been generated for max. ${maxargs} parameters
 239 $eval_func_interface
 240 $evalf_func_interface
 241 $derivative_func_interface
 242 $series_func_interface
 243 // end of generated lines
 244         function_options & eval_func(eval_funcp_exvector e);
 245         function_options & evalf_func(evalf_funcp_exvector ef);
 246         function_options & derivative_func(derivative_funcp_exvector d);
 247         function_options & series_func(series_funcp_exvector s);
 248
 249         function_options & set_return_type(unsigned rt, unsigned rtt=0);
 250         function_options & do_not_evalf_params();
 251         function_options & remember(unsigned size, unsigned assoc_size=0,
 252                                     unsigned strategy=remember_strategies::delete_never);
 253         function_options & overloaded(unsigned o);
 254         function_options & set_symmetry(const symmetry & s);
 255         void test_and_set_nparams(unsigned n);
 256         std::string get_name() const { return name; }
 257         unsigned get_nparams() const { return nparams; }
 258         bool has_derivative() const { return derivative_f != NULL; }
 259
 260 protected:
 261         std::string name;
 262         std::string TeX_name;
 263
 264         unsigned nparams;
 265
 266         eval_funcp eval_f;
 267         evalf_funcp evalf_f;
 268         derivative_funcp derivative_f;
 269         series_funcp series_f;
 270
 271         bool evalf_params_first;
 272
 273         bool use_return_type;
 274         unsigned return_type;
 275         unsigned return_type_tinfo;
 276
 277         bool use_remember;
 278         unsigned remember_size;
 279         unsigned remember_assoc_size;
 280         unsigned remember_strategy;
 281
 282         bool eval_use_exvector_args;
 283         bool evalf_use_exvector_args;
 284         bool derivative_use_exvector_args;
 285         bool series_use_exvector_args;
 286
 287         unsigned functions_with_same_name;
 288
 289         ex symtree;
 290 };
 291
 292
 293 /** Exception class thrown by classes which provide their own series expansion
 294  *  to signal that ordinary Taylor expansion is safe. */
 295 class do_taylor {};
 296
 297
 298 /** The class function is used to implement builtin functions like sin, cos...
 299         and user defined functions */
 300 class function : public exprseq
 301 {
 302         GINAC_DECLARE_REGISTERED_CLASS(function, exprseq)
 303
 304         // CINT has a linking problem
 305 #ifndef __MAKECINT__
 306         friend void ginsh_get_ginac_functions();
 307 #endif // def __MAKECINT__
 308
 309         friend class remember_table_entry;
 310         // friend class remember_table_list;
 311         // friend class remember_table;
 312
 313 // member functions
 314
 315         // other constructors
 316 public:
 317         function(unsigned ser);
 318         // the following lines have been generated for max. ${maxargs} parameters
 319 $constructors_interface
 320         // end of generated lines
 321         function(unsigned ser, const exprseq & es);
 322         function(unsigned ser, const exvector & v, bool discardable = false);
 323         function(unsigned ser, exvector * vp); // vp will be deleted
 324
 325         // functions overriding virtual functions from base classes
 326 public:
 327         void print(const print_context & c, unsigned level = 0) const;
 328         unsigned precedence() const {return 70;}
 329         ex expand(unsigned options=0) const;
 330         ex eval(int level=0) const;
 331         ex evalf(int level=0) const;
 332         unsigned calchash() const;
 333         ex series(const relational & r, int order, unsigned options = 0) const;
 334         ex thiscontainer(const exvector & v) const;
 335         ex thiscontainer(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() const;
 341         unsigned return_type_tinfo() 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();
 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 current_serial;
 355         static unsigned find_function(const std::string &name, unsigned nparams);
 356         unsigned get_serial() const {return serial;}
 357         std::string get_name() const;
 358
 359 // member variables
 360
 361 protected:
 362         unsigned serial;
 363 };
 364
 365 // utility functions/macros
 366
 367 /** Specialization of is_exactly_a<function>(obj) for objects of type function. */
 368 template<> inline bool is_exactly_a<function>(const basic & obj)
 369 {
 370         return obj.tinfo()==TINFO_function;
 371 }
 372
 373 template <typename T>
 374 inline bool is_the_function(const ex & x)
 375 {
 376         return is_exactly_a<function>(x)
 377             && ex_to<function>(x).get_serial() == T::serial;
 378 }
 379
 380 // Check whether OBJ is the specified symbolic function.
 381 #define is_ex_the_function(OBJ, FUNCNAME) (GiNaC::is_the_function<FUNCNAME##_SERIAL>(OBJ))
 382
 383 } // namespace GiNaC
 384
 385 #endif // ndef __GINAC_FUNCTION_H__
 386
 387 END_OF_INTERFACE
 388
 389 $implementation=<<END_OF_IMPLEMENTATION;
 390 /** \@file function.cpp
 391  *
 392  *  Implementation of class of symbolic functions. */
 393
 394 /*
 395  *  This file was generated automatically by function.pl.
 396  *  Please do not modify it directly, edit the perl script instead!
 397  *  function.pl options: \$maxargs=${maxargs}
 398  *
 399  *  GiNaC Copyright (C) 1999-2003 Johannes Gutenberg University Mainz, Germany
 400  *
 401  *  This program is free software; you can redistribute it and/or modify
 402  *  it under the terms of the GNU General Public License as published by
 403  *  the Free Software Foundation; either version 2 of the License, or
 404  *  (at your option) any later version.
 405  *
 406  *  This program is distributed in the hope that it will be useful,
 407  *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 408  *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 409  *  GNU General Public License for more details.
 410  *
 411  *  You should have received a copy of the GNU General Public License
 412  *  along with this program; if not, write to the Free Software
 413  *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 414  */
 415
 416 #include <iostream>
 417 #include <string>
 418 #include <stdexcept>
 419 #include <list>
 420
 421 #include "function.h"
 422 #include "operators.h"
 423 #include "fderivative.h"
 424 #include "ex.h"
 425 #include "lst.h"
 426 #include "symmetry.h"
 427 #include "print.h"
 428 #include "archive.h"
 429 #include "inifcns.h"
 430 #include "tostring.h"
 431 #include "utils.h"
 432 #include "remember.h"
 433
 434 namespace GiNaC {
 435
 436 //////////
 437 // helper class function_options
 438 //////////
 439
 440 function_options::function_options()
 441 {
 442         initialize();
 443 }
 444
 445 function_options::function_options(std::string const & n, std::string const & tn)
 446 {
 447         initialize();
 448         set_name(n,tn);
 449 }
 450
 451 function_options::~function_options()
 452 {
 453         // nothing to clean up at the moment
 454 }
 455
 456 void function_options::initialize()
 457 {
 458         set_name("unnamed_function","\\\\mbox{unnamed}");
 459         nparams = 0;
 460         eval_f = evalf_f = derivative_f = series_f = 0;
 461         evalf_params_first = true;
 462         use_return_type = false;
 463         eval_use_exvector_args = false;
 464         evalf_use_exvector_args = false;
 465         derivative_use_exvector_args = false;
 466         series_use_exvector_args = false;
 467         use_remember = false;
 468         functions_with_same_name = 1;
 469         symtree = 0;
 470 }
 471
 472 function_options & function_options::set_name(std::string const & n,
 473                                               std::string const & tn)
 474 {
 475         name = n;
 476         if (tn==std::string())
 477                 TeX_name = "\\\\mbox{"+name+"}";
 478         else
 479                 TeX_name = tn;
 480         return *this;
 481 }
 482
 483 function_options & function_options::latex_name(std::string const & tn)
 484 {
 485         TeX_name = tn;
 486         return *this;
 487 }
 488
 489 // the following lines have been generated for max. ${maxargs} parameters
 490 $eval_func_implementation
 491 $evalf_func_implementation
 492 $derivative_func_implementation
 493 $series_func_implementation
 494 // end of generated lines
 495
 496 function_options& function_options::eval_func(eval_funcp_exvector e)
 497 {
 498         eval_use_exvector_args = true;
 499         eval_f = eval_funcp(e);
 500         return *this;
 501 }
 502 function_options& function_options::evalf_func(evalf_funcp_exvector ef)
 503 {
 504         evalf_use_exvector_args = true;
 505         evalf_f = evalf_funcp(ef);
 506         return *this;
 507 }
 508 function_options& function_options::derivative_func(derivative_funcp_exvector d)
 509 {
 510         derivative_use_exvector_args = true;
 511         derivative_f = derivative_funcp(d);
 512         return *this;
 513 }
 514 function_options& function_options::series_func(series_funcp_exvector s)
 515 {
 516         series_use_exvector_args = true;
 517         series_f = series_funcp(s);
 518         return *this;
 519 }
 520
 521 function_options & function_options::set_return_type(unsigned rt, unsigned rtt)
 522 {
 523         use_return_type = true;
 524         return_type = rt;
 525         return_type_tinfo = rtt;
 526         return *this;
 527 }
 528
 529 function_options & function_options::do_not_evalf_params()
 530 {
 531         evalf_params_first = false;
 532         return *this;
 533 }
 534
 535 function_options & function_options::remember(unsigned size,
 536                                               unsigned assoc_size,
 537                                               unsigned strategy)
 538 {
 539         use_remember = true;
 540         remember_size = size;
 541         remember_assoc_size = assoc_size;
 542         remember_strategy = strategy;
 543         return *this;
 544 }
 545
 546 function_options & function_options::overloaded(unsigned o)
 547 {
 548         functions_with_same_name = o;
 549         return *this;
 550 }
 551
 552 function_options & function_options::set_symmetry(const symmetry & s)
 553 {
 554         symtree = s;
 555         return *this;
 556 }
 557
 558 void function_options::test_and_set_nparams(unsigned n)
 559 {
 560         if (nparams==0) {
 561                 nparams = n;
 562         } else if (nparams!=n) {
 563                 // we do not throw an exception here because this code is
 564                 // usually executed before main(), so the exception could not
 565                 // caught anyhow
 566                 std::cerr << "WARNING: " << name << "(): number of parameters ("
 567                           << n << ") differs from number set before ("
 568                           << nparams << ")" << std::endl;
 569         }
 570 }
 571
 572 /** This can be used as a hook for external applications. */
 573 unsigned function::current_serial = 0;
 574
 575
 576 GINAC_IMPLEMENT_REGISTERED_CLASS(function, exprseq)
 577
 578 //////////
 579 // default constructor
 580 //////////
 581
 582 // public
 583
 584 function::function() : serial(0)
 585 {
 586         tinfo_key = TINFO_function;
 587 }
 588
 589 //////////
 590 // other constructors
 591 //////////
 592
 593 // public
 594
 595 function::function(unsigned ser) : serial(ser)
 596 {
 597         tinfo_key = TINFO_function;
 598 }
 599
 600 // the following lines have been generated for max. ${maxargs} parameters
 601 $constructors_implementation
 602 // end of generated lines
 603
 604 function::function(unsigned ser, const exprseq & es) : exprseq(es), serial(ser)
 605 {
 606         tinfo_key = TINFO_function;
 607
 608         // Force re-evaluation even if the exprseq was already evaluated
 609         // (the exprseq copy constructor copies the flags)
 610         clearflag(status_flags::evaluated);
 611 }
 612
 613 function::function(unsigned ser, const exvector & v, bool discardable)
 614   : exprseq(v,discardable), serial(ser)
 615 {
 616         tinfo_key = TINFO_function;
 617 }
 618
 619 function::function(unsigned ser, exvector * vp)
 620   : exprseq(vp), serial(ser)
 621 {
 622         tinfo_key = TINFO_function;
 623 }
 624
 625 //////////
 626 // archiving
 627 //////////
 628
 629 /** Construct object from archive_node. */
 630 function::function(const archive_node &n, lst &sym_lst) : inherited(n, sym_lst)
 631 {
 632         // Find serial number by function name
 633         std::string s;
 634         if (n.find_string("name", s)) {
 635                 unsigned int ser = 0;
 636                 std::vector<function_options>::const_iterator i = registered_functions().begin(), iend = registered_functions().end();
 637                 while (i != iend) {
 638                         if (s == i->name) {
 639                                 serial = ser;
 640                                 return;
 641                         }
 642                         ++i; ++ser;
 643                 }
 644                 throw (std::runtime_error("unknown function '" + s + "' in archive"));
 645         } else
 646                 throw (std::runtime_error("unnamed function in archive"));
 647 }
 648
 649 /** Unarchive the object. */
 650 ex function::unarchive(const archive_node &n, lst &sym_lst)
 651 {
 652         return (new function(n, sym_lst))->setflag(status_flags::dynallocated);
 653 }
 654
 655 /** Archive the object. */
 656 void function::archive(archive_node &n) const
 657 {
 658         inherited::archive(n);
 659         GINAC_ASSERT(serial < registered_functions().size());
 660         n.add_string("name", registered_functions()[serial].name);
 661 }
 662
 663 //////////
 664 // functions overriding virtual functions from base classes
 665 //////////
 666
 667 // public
 668
 669 void function::print(const print_context & c, unsigned level) const
 670 {
 671         GINAC_ASSERT(serial<registered_functions().size());
 672
 673         if (is_a<print_tree>(c)) {
 674
 675                 c.s << std::string(level, ' ') << class_name() << " "
 676                     << registered_functions()[serial].name
 677                     << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
 678                     << ", nops=" << nops()
 679                     << std::endl;
 680                 unsigned delta_indent = static_cast<const print_tree &>(c).delta_indent;
 681                 for (size_t i=0; i<seq.size(); ++i)
 682                         seq[i].print(c, level + delta_indent);
 683                 c.s << std::string(level + delta_indent, ' ') << "=====" << std::endl;
 684
 685         } else if (is_a<print_csrc>(c)) {
 686
 687                 // Print function name in lowercase
 688                 std::string lname = registered_functions()[serial].name;
 689                 size_t num = lname.size();
 690                 for (size_t i=0; i<num; i++)
 691                         lname[i] = tolower(lname[i]);
 692                 c.s << lname << "(";
 693
 694                 // Print arguments, separated by commas
 695                 exvector::const_iterator it = seq.begin(), itend = seq.end();
 696                 while (it != itend) {
 697                         it->print(c);
 698                         ++it;
 699                         if (it != itend)
 700                                 c.s << ",";
 701                 }
 702                 c.s << ")";
 703
 704         } else if (is_a<print_latex>(c)) {
 705                 c.s << registered_functions()[serial].TeX_name;
 706                 printseq(c, '(', ',', ')', exprseq::precedence(), function::precedence());
 707         } else {
 708                 c.s << registered_functions()[serial].name;
 709                 printseq(c, '(', ',', ')', exprseq::precedence(), function::precedence());
 710         }
 711 }
 712
 713 ex function::expand(unsigned options) const
 714 {
 715         // Only expand arguments when asked to do so
 716         if (options & expand_options::expand_function_args)
 717                 return inherited::expand(options);
 718         else
 719                 return (options == 0) ? setflag(status_flags::expanded) : *this;
 720 }
 721
 722 ex function::eval(int level) const
 723 {
 724         GINAC_ASSERT(serial<registered_functions().size());
 725
 726         if (level>1) {
 727                 // first evaluate children, then we will end up here again
 728                 return function(serial,evalchildren(level));
 729         }
 730
 731         const function_options &opt = registered_functions()[serial];
 732
 733         // Canonicalize argument order according to the symmetry properties
 734         if (seq.size() > 1 && !(opt.symtree.is_zero())) {
 735                 exvector v = seq;
 736                 GINAC_ASSERT(is_a<symmetry>(opt.symtree));
 737                 int sig = canonicalize(v.begin(), ex_to<symmetry>(opt.symtree));
 738                 if (sig != INT_MAX) {
 739                         // Something has changed while sorting arguments, more evaluations later
 740                         if (sig == 0)
 741                                 return _ex0;
 742                         return ex(sig) * thiscontainer(v);
 743                 }
 744         }
 745
 746         if (opt.eval_f==0) {
 747                 return this->hold();
 748         }
 749
 750         bool use_remember = opt.use_remember;
 751         ex eval_result;
 752         if (use_remember && lookup_remember_table(eval_result)) {
 753                 return eval_result;
 754         }
 755         current_serial = serial;
 756         if (registered_functions()[serial].eval_use_exvector_args)
 757                 eval_result = ((eval_funcp_exvector)(registered_functions()[serial].eval_f))(seq);
 758         else
 759         switch (opt.nparams) {
 760                 // the following lines have been generated for max. ${maxargs} parameters
 761 ${eval_switch_statement}
 762                 // end of generated lines
 763         default:
 764                 throw(std::logic_error("function::eval(): invalid nparams"));
 765         }
 766         if (use_remember) {
 767                 store_remember_table(eval_result);
 768         }
 769         return eval_result;
 770 }
 771
 772 ex function::evalf(int level) const
 773 {
 774         GINAC_ASSERT(serial<registered_functions().size());
 775
 776         const function_options &opt = registered_functions()[serial];
 777
 778         // Evaluate children first
 779         exvector eseq;
 780         if (level == 1 || !(opt.evalf_params_first))
 781                 eseq = seq;
 782         else if (level == -max_recursion_level)
 783                 throw(std::runtime_error("max recursion level reached"));
 784         else {
 785                 eseq.reserve(seq.size());
 786                 --level;
 787                 exvector::const_iterator it = seq.begin(), itend = seq.end();
 788                 while (it != itend) {
 789                         eseq.push_back(it->evalf(level));
 790                         ++it;
 791                 }
 792         }
 793
 794         if (opt.evalf_f==0) {
 795                 return function(serial,eseq).hold();
 796         }
 797         current_serial = serial;
 798         if (opt.evalf_use_exvector_args)
 799                 return ((evalf_funcp_exvector)(opt.evalf_f))(seq);
 800         switch (opt.nparams) {
 801                 // the following lines have been generated for max. ${maxargs} parameters
 802 ${evalf_switch_statement}
 803                 // end of generated lines
 804         }
 805         throw(std::logic_error("function::evalf(): invalid nparams"));
 806 }
 807
 808 unsigned function::calchash() const
 809 {
 810         unsigned v = golden_ratio_hash(golden_ratio_hash(tinfo()) ^ serial);
 811         for (size_t i=0; i<nops(); i++) {
 812                 v = rotate_left(v);
 813                 v ^= this->op(i).gethash();
 814         }
 815
 816         if (flags & status_flags::evaluated) {
 817                 setflag(status_flags::hash_calculated);
 818                 hashvalue = v;
 819         }
 820         return v;
 821 }
 822
 823 ex function::thiscontainer(const exvector & v) const
 824 {
 825         return function(serial,v);
 826 }
 827
 828 ex function::thiscontainer(exvector * vp) const
 829 {
 830         return function(serial,vp);
 831 }
 832
 833 /** Implementation of ex::series for functions.
 834  *  \@see ex::series */
 835 ex function::series(const relational & r, int order, unsigned options) const
 836 {
 837         GINAC_ASSERT(serial<registered_functions().size());
 838
 839         if (registered_functions()[serial].series_f==0) {
 840                 return basic::series(r, order);
 841         }
 842         ex res;
 843         current_serial = serial;
 844         if (registered_functions()[serial].series_use_exvector_args) {
 845                 try {
 846                         res = ((series_funcp_exvector)(registered_functions()[serial].series_f))(seq, r, order, options);
 847                 } catch (do_taylor) {
 848                         res = basic::series(r, order, options);
 849                 }
 850                 return res;
 851         }
 852         switch (registered_functions()[serial].nparams) {
 853                 // the following lines have been generated for max. ${maxargs} parameters
 854 ${series_switch_statement}
 855                 // end of generated lines
 856         }
 857         throw(std::logic_error("function::series(): invalid nparams"));
 858 }
 859
 860 // protected
 861
 862 /** Implementation of ex::diff() for functions. It applies the chain rule,
 863  *  except for the Order term function.
 864  *  \@see ex::diff */
 865 ex function::derivative(const symbol & s) const
 866 {
 867         ex result;
 868
 869         if (serial == Order_SERIAL::serial) {
 870                 // Order Term function only differentiates the argument
 871                 return Order(seq[0].diff(s));
 872         } else {
 873                 // Chain rule
 874                 ex arg_diff;
 875                 size_t num = seq.size();
 876                 for (size_t i=0; i<num; i++) {
 877                         arg_diff = seq[i].diff(s);
 878                         // We apply the chain rule only when it makes sense.  This is not
 879                         // just for performance reasons but also to allow functions to
 880                         // throw when differentiated with respect to one of its arguments
 881                         // without running into trouble with our automatic full
 882                         // differentiation:
 883                         if (!arg_diff.is_zero())
 884                                 result += pderivative(i)*arg_diff;
 885                 }
 886         }
 887         return result;
 888 }
 889
 890 int function::compare_same_type(const basic & other) const
 891 {
 892         GINAC_ASSERT(is_a<function>(other));
 893         const function & o = static_cast<const function &>(other);
 894
 895         if (serial != o.serial)
 896                 return serial < o.serial ? -1 : 1;
 897         else
 898                 return exprseq::compare_same_type(o);
 899 }
 900
 901 bool function::is_equal_same_type(const basic & other) const
 902 {
 903         GINAC_ASSERT(is_a<function>(other));
 904         const function & o = static_cast<const function &>(other);
 905
 906         if (serial != o.serial)
 907                 return false;
 908         else
 909                 return exprseq::is_equal_same_type(o);
 910 }
 911
 912 bool function::match_same_type(const basic & other) const
 913 {
 914         GINAC_ASSERT(is_a<function>(other));
 915         const function & o = static_cast<const function &>(other);
 916
 917         return serial == o.serial;
 918 }
 919
 920 unsigned function::return_type() const
 921 {
 922         const function_options &opt = registered_functions()[serial];
 923
 924         if (opt.use_return_type) {
 925                 // Return type was explicitly specified
 926                 return opt.return_type;
 927         } else {
 928                 // Default behavior is to use the return type of the first
 929                 // argument. Thus, exp() of a matrix behaves like a matrix, etc.
 930                 if (seq.empty())
 931                         return return_types::commutative;
 932                 else
 933                         return seq.begin()->return_type();
 934         }
 935 }
 936
 937 unsigned function::return_type_tinfo() const
 938 {
 939         const function_options &opt = registered_functions()[serial];
 940
 941         if (opt.use_return_type) {
 942                 // Return type was explicitly specified
 943                 return opt.return_type_tinfo;
 944         } else {
 945                 // Default behavior is to use the return type of the first
 946                 // argument. Thus, exp() of a matrix behaves like a matrix, etc.
 947                 if (seq.empty())
 948                         return tinfo_key;
 949                 else
 950                         return seq.begin()->return_type_tinfo();
 951         }
 952 }
 953
 954 //////////
 955 // new virtual functions which can be overridden by derived classes
 956 //////////
 957
 958 // none
 959
 960 //////////
 961 // non-virtual functions in this class
 962 //////////
 963
 964 // protected
 965
 966 ex function::pderivative(unsigned diff_param) const // partial differentiation
 967 {
 968         GINAC_ASSERT(serial<registered_functions().size());
 969
 970         // No derivative defined? Then return abstract derivative object
 971         if (registered_functions()[serial].derivative_f == NULL)
 972                 return fderivative(serial, diff_param, seq);
 973
 974         current_serial = serial;
 975         if (registered_functions()[serial].derivative_use_exvector_args)
 976                 return ((derivative_funcp_exvector)(registered_functions()[serial].derivative_f))(seq, diff_param);
 977         switch (registered_functions()[serial].nparams) {
 978                 // the following lines have been generated for max. ${maxargs} parameters
 979 ${diff_switch_statement}
 980                 // end of generated lines
 981         }
 982         throw(std::logic_error("function::pderivative(): no diff function defined"));
 983 }
 984
 985 std::vector<function_options> & function::registered_functions()
 986 {
 987         static std::vector<function_options> * rf = new std::vector<function_options>;
 988         return *rf;
 989 }
 990
 991 bool function::lookup_remember_table(ex & result) const
 992 {
 993         return remember_table::remember_tables()[serial].lookup_entry(*this,result);
 994 }
 995
 996 void function::store_remember_table(ex const & result) const
 997 {
 998         remember_table::remember_tables()[serial].add_entry(*this,result);
 999 }
1000
1001 // public
1002
1003 unsigned function::register_new(function_options const & opt)
1004 {
1005         size_t same_name = 0;
1006         for (size_t i=0; i<registered_functions().size(); ++i) {
1007                 if (registered_functions()[i].name==opt.name) {
1008                         ++same_name;
1009                 }
1010         }
1011         if (same_name>=opt.functions_with_same_name) {
1012                 // we do not throw an exception here because this code is
1013                 // usually executed before main(), so the exception could not
1014                 // caught anyhow
1015                 std::cerr << "WARNING: function name " << opt.name
1016                           << " already in use!" << std::endl;
1017         }
1018         registered_functions().push_back(opt);
1019         if (opt.use_remember) {
1020                 remember_table::remember_tables().
1021                         push_back(remember_table(opt.remember_size,
1022                                                  opt.remember_assoc_size,
1023                                                  opt.remember_strategy));
1024         } else {
1025                 remember_table::remember_tables().push_back(remember_table());
1026         }
1027         return registered_functions().size()-1;
1028 }
1029
1030 /** Find serial number of function by name and number of parameters.
1031  *  Throws exception if function was not found. */
1032 unsigned function::find_function(const std::string &name, unsigned nparams)
1033 {
1034         std::vector<function_options>::const_iterator i = function::registered_functions().begin(), end = function::registered_functions().end();
1035         unsigned serial = 0;
1036         while (i != end) {
1037                 if (i->get_name() == name && i->get_nparams() == nparams)
1038                         return serial;
1039                 ++i;
1040                 ++serial;
1041         }
1042         throw (std::runtime_error("no function '" + name + "' with " + ToString(nparams) + " parameters defined"));
1043 }
1044
1045 /** Return the print name of the function. */
1046 std::string function::get_name() const
1047 {
1048         GINAC_ASSERT(serial<registered_functions().size());
1049         return registered_functions()[serial].name;
1050 }
1051
1052 } // namespace GiNaC
1053
1054 END_OF_IMPLEMENTATION
1055
1056 print "Creating interface file function.h...";
1057 open OUT,">function.h" or die "cannot open function.h";
1058 print OUT $interface;
1059 close OUT;
1060 print "ok.\n";
1061
1062 print "Creating implementation file function.cpp...";
1063 open OUT,">function.cpp" or die "cannot open function.cpp";
1064 print OUT $implementation;
1065 close OUT;
1066 print "ok.\n";
1067
1068 print "done.\n";