ginac/function.pl

   1 $maxargs=13;
   2
   3 sub generate_seq {
   4         my ($seq_template,$n)=@_;
   5         my ($res,$N);
   6
   7         $res='';
   8         for ($N=1; $N<=$n; $N++) {
   9                 $res .= eval('"' . $seq_template . '"');
  10                 if ($N!=$n) {
  11                         $res .= ', ';
  12                 }
  13         }
  14         return $res;
  15 }
  16
  17 sub generate_from_to {
  18         my ($template,$seq_template1,$seq_template2,$seq_template3,$from,$to)=@_;
  19         my ($res,$N,$SEQ);
  20
  21         $res='';
  22         for ($N=$from; $N<=$to; $N++) {
  23                 $SEQ1=generate_seq($seq_template1,$N);
  24                 $SEQ2=generate_seq($seq_template2,$N);
  25                 $SEQ3=generate_seq($seq_template3,$N);
  26                 $res .= eval('"' . $template . '"');
  27                 $SEQ1=''; # to avoid main::SEQ1 used only once warning
  28                 $SEQ2=''; # same as above
  29                 $SEQ3=''; # same as above
  30         }
  31         return $res;
  32 }
  33
  34 sub generate {
  35         my ($template,$seq_template1,$seq_template2,$seq_template3)=@_;
  36         return generate_from_to($template,$seq_template1,$seq_template2,$seq_template3,1,$maxargs);
  37 }
  38
  39 $declare_function_macro = generate(
  40         <<'END_OF_DECLARE_FUNCTION_MACRO','typename T${N}','const T${N} & p${N}','GiNaC::ex(p${N})');
  41 #define DECLARE_FUNCTION_${N}P(NAME) \\
  42 extern const unsigned function_index_##NAME; \\
  43 template<${SEQ1}> \\
  44 inline const GiNaC::function NAME(${SEQ2}) { \\
  45         return GiNaC::function(function_index_##NAME, ${SEQ3}); \\
  46 }
  47
  48 END_OF_DECLARE_FUNCTION_MACRO
  49
  50 $typedef_eval_funcp=generate(
  51 'typedef ex (* eval_funcp_${N})(${SEQ1});'."\n",
  52 'const ex &','','');
  53
  54 $typedef_evalf_funcp=generate(
  55 'typedef ex (* evalf_funcp_${N})(${SEQ1});'."\n",
  56 'const ex &','','');
  57
  58 $typedef_derivative_funcp=generate(
  59 'typedef ex (* derivative_funcp_${N})(${SEQ1}, unsigned);'."\n",
  60 'const ex &','','');
  61
  62 $typedef_series_funcp=generate(
  63 'typedef ex (* series_funcp_${N})(${SEQ1}, const relational &, int, unsigned);'."\n",
  64 'const ex &','','');
  65
  66 $eval_func_interface=generate('    function_options & eval_func(eval_funcp_${N} e);'."\n",'','','');
  67
  68 $evalf_func_interface=generate('    function_options & evalf_func(evalf_funcp_${N} ef);'."\n",'','','');
  69
  70 $derivative_func_interface=generate('    function_options & derivative_func(derivative_funcp_${N} d);'."\n",'','','');
  71
  72 $series_func_interface=generate('    function_options & series_func(series_funcp_${N} s);'."\n",'','','');
  73
  74 $constructors_interface=generate(
  75 '    function(unsigned ser, ${SEQ1});'."\n",
  76 'const ex & param${N}','','');
  77
  78 $constructors_implementation=generate(
  79         <<'END_OF_CONSTRUCTORS_IMPLEMENTATION','const ex & param${N}','param${N}','');
  80 function::function(unsigned ser, ${SEQ1})
  81         : exprseq(${SEQ2}), serial(ser)
  82 {
  83         tinfo_key = TINFO_function;
  84 }
  85 END_OF_CONSTRUCTORS_IMPLEMENTATION
  86
  87 $eval_switch_statement=generate(
  88         <<'END_OF_EVAL_SWITCH_STATEMENT','seq[${N}-1]','','');
  89         case ${N}:
  90                 eval_result = ((eval_funcp_${N})(registered_functions()[serial].eval_f))(${SEQ1});
  91                 break;
  92 END_OF_EVAL_SWITCH_STATEMENT
  93
  94 $evalf_switch_statement=generate(
  95         <<'END_OF_EVALF_SWITCH_STATEMENT','eseq[${N}-1]','','');
  96         case ${N}:
  97                 return ((evalf_funcp_${N})(registered_functions()[serial].evalf_f))(${SEQ1});
  98 END_OF_EVALF_SWITCH_STATEMENT
  99
 100 $diff_switch_statement=generate(
 101         <<'END_OF_DIFF_SWITCH_STATEMENT','seq[${N}-1]','','');
 102         case ${N}:
 103                 return ((derivative_funcp_${N})(registered_functions()[serial].derivative_f))(${SEQ1},diff_param);
 104 END_OF_DIFF_SWITCH_STATEMENT
 105
 106 $series_switch_statement=generate(
 107         <<'END_OF_SERIES_SWITCH_STATEMENT','seq[${N}-1]','','');
 108         case ${N}:
 109                 try {
 110                         res = ((series_funcp_${N})(registered_functions()[serial].series_f))(${SEQ1},r,order,options);
 111                 } catch (do_taylor) {
 112                         res = basic::series(r, order, options);
 113                 }
 114                 return res;
 115 END_OF_SERIES_SWITCH_STATEMENT
 116
 117 $eval_func_implementation=generate(
 118         <<'END_OF_EVAL_FUNC_IMPLEMENTATION','','','');
 119 function_options & function_options::eval_func(eval_funcp_${N} e)
 120 {
 121         test_and_set_nparams(${N});
 122         eval_f = eval_funcp(e);
 123         return *this;
 124 }
 125 END_OF_EVAL_FUNC_IMPLEMENTATION
 126
 127 $evalf_func_implementation=generate(
 128         <<'END_OF_EVALF_FUNC_IMPLEMENTATION','','','');
 129 function_options & function_options::evalf_func(evalf_funcp_${N} ef)
 130 {
 131         test_and_set_nparams(${N});
 132         evalf_f = evalf_funcp(ef);
 133         return *this;
 134 }
 135 END_OF_EVALF_FUNC_IMPLEMENTATION
 136
 137 $derivative_func_implementation=generate(
 138         <<'END_OF_DERIVATIVE_FUNC_IMPLEMENTATION','','','');
 139 function_options & function_options::derivative_func(derivative_funcp_${N} d)
 140 {
 141         test_and_set_nparams(${N});
 142         derivative_f = derivative_funcp(d);
 143         return *this;
 144 }
 145 END_OF_DERIVATIVE_FUNC_IMPLEMENTATION
 146
 147 $series_func_implementation=generate(
 148         <<'END_OF_SERIES_FUNC_IMPLEMENTATION','','','');
 149 function_options & function_options::series_func(series_funcp_${N} s)
 150 {
 151         test_and_set_nparams(${N});
 152         series_f = series_funcp(s);
 153         return *this;
 154 }
 155 END_OF_SERIES_FUNC_IMPLEMENTATION
 156
 157 $interface=<<END_OF_INTERFACE;
 158 /** \@file function.h
 159  *
 160  *  Interface to class of symbolic functions. */
 161
 162 /*
 163  *  This file was generated automatically by function.pl.
 164  *  Please do not modify it directly, edit the perl script instead!
 165  *  function.pl options: \$maxargs=${maxargs}
 166  *
 167  *  GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
 168  *
 169  *  This program is free software; you can redistribute it and/or modify
 170  *  it under the terms of the GNU General Public License as published by
 171  *  the Free Software Foundation; either version 2 of the License, or
 172  *  (at your option) any later version.
 173  *
 174  *  This program is distributed in the hope that it will be useful,
 175  *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 176  *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 177  *  GNU General Public License for more details.
 178  *
 179  *  You should have received a copy of the GNU General Public License
 180  *  along with this program; if not, write to the Free Software
 181  *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 182  */
 183
 184 #ifndef __GINAC_FUNCTION_H__
 185 #define __GINAC_FUNCTION_H__
 186
 187 #include <string>
 188 #include <vector>
 189
 190 // CINT needs <algorithm> to work properly with <vector>
 191 #include <algorithm>
 192
 193 #include "exprseq.h"
 194
 195 // the following lines have been generated for max. ${maxargs} parameters
 196 $declare_function_macro
 197 // end of generated lines
 198
 199 #define REGISTER_FUNCTION(NAME,OPT) \\
 200 const unsigned function_index_##NAME= \\
 201         GiNaC::function::register_new(GiNaC::function_options(#NAME).OPT);
 202
 203 namespace GiNaC {
 204
 205 class function;
 206 class symmetry;
 207
 208 typedef ex (* eval_funcp)();
 209 typedef ex (* evalf_funcp)();
 210 typedef ex (* derivative_funcp)();
 211 typedef ex (* series_funcp)();
 212
 213 // the following lines have been generated for max. ${maxargs} parameters
 214 $typedef_eval_funcp
 215 $typedef_evalf_funcp
 216 $typedef_derivative_funcp
 217 $typedef_series_funcp
 218 // end of generated lines
 219
 220 // Alternatively, an exvector may be passed into the static function, instead
 221 // of individual ex objects.  Then, the number of arguments is not limited.
 222 typedef ex (* eval_funcp_exvector)(const exvector &);
 223 typedef ex (* evalf_funcp_exvector)(const exvector &);
 224 typedef ex (* derivative_funcp_exvector)(const exvector &, unsigned);
 225 typedef ex (* series_funcp_exvector)(const exvector &, const relational &, int, unsigned);
 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(void);
 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(void);
 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(void) const { return name; }
 257         unsigned get_nparams(void) const { return nparams; }
 258         bool has_derivative(void) 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 /** The class function is used to implement builtin functions like sin, cos...
 293         and user defined functions */
 294 class function : public exprseq
 295 {
 296         GINAC_DECLARE_REGISTERED_CLASS(function, exprseq)
 297
 298         // CINT has a linking problem
 299 #ifndef __MAKECINT__
 300         friend void ginsh_get_ginac_functions(void);
 301 #endif // def __MAKECINT__
 302
 303         friend class remember_table_entry;
 304         // friend class remember_table_list;
 305         // friend class remember_table;
 306
 307 // member functions
 308
 309         // other ctors
 310 public:
 311         function(unsigned ser);
 312         // the following lines have been generated for max. ${maxargs} parameters
 313 $constructors_interface
 314         // end of generated lines
 315         function(unsigned ser, const exprseq & es);
 316         function(unsigned ser, const exvector & v, bool discardable = false);
 317         function(unsigned ser, exvector * vp); // vp will be deleted
 318
 319         // functions overriding virtual functions from base classes
 320 public:
 321         void print(const print_context & c, unsigned level = 0) const;
 322         unsigned precedence(void) const {return 70;}
 323         int degree(const ex & s) const;
 324         int ldegree(const ex & s) const;
 325         ex coeff(const ex & s, int n = 1) const;
 326         ex expand(unsigned options=0) const;
 327         ex eval(int level=0) const;
 328         ex evalf(int level=0) const;
 329         unsigned calchash(void) const;
 330         ex series(const relational & r, int order, unsigned options = 0) const;
 331         ex thisexprseq(const exvector & v) const;
 332         ex thisexprseq(exvector * vp) const;
 333 protected:
 334         ex derivative(const symbol & s) const;
 335         bool is_equal_same_type(const basic & other) const;
 336         bool match_same_type(const basic & other) const;
 337         unsigned return_type(void) const;
 338         unsigned return_type_tinfo(void) const;
 339
 340         // new virtual functions which can be overridden by derived classes
 341         // none
 342
 343         // non-virtual functions in this class
 344 protected:
 345         ex pderivative(unsigned diff_param) const; // partial differentiation
 346         static std::vector<function_options> & registered_functions(void);
 347         bool lookup_remember_table(ex & result) const;
 348         void store_remember_table(ex const & result) const;
 349 public:
 350         static unsigned register_new(function_options const & opt);
 351         static unsigned current_serial;
 352         static unsigned find_function(const std::string &name, unsigned nparams);
 353         unsigned get_serial(void) const {return serial;}
 354         std::string get_name(void) const;
 355
 356 // member variables
 357
 358 protected:
 359         unsigned serial;
 360 };
 361
 362 // utility functions/macros
 363
 364 /** Specialization of is_exactly_a<function>(obj) for objects of type function. */
 365 template<> inline bool is_exactly_a<function>(const basic & obj)
 366 {
 367         return obj.tinfo()==TINFO_function;
 368 }
 369
 370 #define is_ex_the_function(OBJ, FUNCNAME) \\
 371         (is_exactly_a<GiNaC::function>(OBJ) && ex_to<GiNaC::function>(OBJ).get_serial() == function_index_##FUNCNAME)
 372
 373 } // namespace GiNaC
 374
 375 #endif // ndef __GINAC_FUNCTION_H__
 376
 377 END_OF_INTERFACE
 378
 379 $implementation=<<END_OF_IMPLEMENTATION;
 380 /** \@file function.cpp
 381  *
 382  *  Implementation of class of symbolic functions. */
 383
 384 /*
 385  *  This file was generated automatically by function.pl.
 386  *  Please do not modify it directly, edit the perl script instead!
 387  *  function.pl options: \$maxargs=${maxargs}
 388  *
 389  *  GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
 390  *
 391  *  This program is free software; you can redistribute it and/or modify
 392  *  it under the terms of the GNU General Public License as published by
 393  *  the Free Software Foundation; either version 2 of the License, or
 394  *  (at your option) any later version.
 395  *
 396  *  This program is distributed in the hope that it will be useful,
 397  *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 398  *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 399  *  GNU General Public License for more details.
 400  *
 401  *  You should have received a copy of the GNU General Public License
 402  *  along with this program; if not, write to the Free Software
 403  *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 404  */
 405
 406 #include <iostream>
 407 #include <string>
 408 #include <stdexcept>
 409 #include <list>
 410
 411 #include "function.h"
 412 #include "fderivative.h"
 413 #include "ex.h"
 414 #include "lst.h"
 415 #include "symmetry.h"
 416 #include "print.h"
 417 #include "archive.h"
 418 #include "inifcns.h"
 419 #include "tostring.h"
 420 #include "utils.h"
 421 #include "remember.h"
 422
 423 namespace GiNaC {
 424
 425 //////////
 426 // helper class function_options
 427 //////////
 428
 429 function_options::function_options()
 430 {
 431         initialize();
 432 }
 433
 434 function_options::function_options(std::string const & n, std::string const & tn)
 435 {
 436         initialize();
 437         set_name(n,tn);
 438 }
 439
 440 function_options::~function_options()
 441 {
 442         // nothing to clean up at the moment
 443 }
 444
 445 void function_options::initialize(void)
 446 {
 447         set_name("unnamed_function","\\\\mbox{unnamed}");
 448         nparams = 0;
 449         eval_f = evalf_f = derivative_f = series_f = 0;
 450         evalf_params_first = true;
 451         use_return_type = false;
 452         eval_use_exvector_args = false;
 453         evalf_use_exvector_args = false;
 454         derivative_use_exvector_args = false;
 455         series_use_exvector_args = false;
 456         use_remember = false;
 457         functions_with_same_name = 1;
 458         symtree = 0;
 459 }
 460
 461 function_options & function_options::set_name(std::string const & n,
 462                                               std::string const & tn)
 463 {
 464         name = n;
 465         if (tn==std::string())
 466                 TeX_name = "\\\\mbox{"+name+"}";
 467         else
 468                 TeX_name = tn;
 469         return *this;
 470 }
 471
 472 function_options & function_options::latex_name(std::string const & tn)
 473 {
 474         TeX_name = tn;
 475         return *this;
 476 }
 477
 478 // the following lines have been generated for max. ${maxargs} parameters
 479 $eval_func_implementation
 480 $evalf_func_implementation
 481 $derivative_func_implementation
 482 $series_func_implementation
 483 // end of generated lines
 484
 485 function_options& function_options::eval_func(eval_funcp_exvector e)
 486 {
 487         eval_use_exvector_args = true;
 488         eval_f = eval_funcp(e);
 489         return *this;
 490 }
 491 function_options& function_options::evalf_func(evalf_funcp_exvector ef)
 492 {
 493         evalf_use_exvector_args = true;
 494         evalf_f = evalf_funcp(ef);
 495         return *this;
 496 }
 497 function_options& function_options::derivative_func(derivative_funcp_exvector d)
 498 {
 499         derivative_use_exvector_args = true;
 500         derivative_f = derivative_funcp(d);
 501         return *this;
 502 }
 503 function_options& function_options::series_func(series_funcp_exvector s)
 504 {
 505         series_use_exvector_args = true;
 506         series_f = series_funcp(s);
 507         return *this;
 508 }
 509
 510
 511 function_options & function_options::set_return_type(unsigned rt, unsigned rtt)
 512 {
 513         use_return_type = true;
 514         return_type = rt;
 515         return_type_tinfo = rtt;
 516         return *this;
 517 }
 518
 519 function_options & function_options::do_not_evalf_params(void)
 520 {
 521         evalf_params_first = false;
 522         return *this;
 523 }
 524
 525 function_options & function_options::remember(unsigned size,
 526                                               unsigned assoc_size,
 527                                               unsigned strategy)
 528 {
 529         use_remember = true;
 530         remember_size = size;
 531         remember_assoc_size = assoc_size;
 532         remember_strategy = strategy;
 533         return *this;
 534 }
 535
 536 function_options & function_options::overloaded(unsigned o)
 537 {
 538         functions_with_same_name = o;
 539         return *this;
 540 }
 541
 542 function_options & function_options::set_symmetry(const symmetry & s)
 543 {
 544         symtree = s;
 545         return *this;
 546 }
 547
 548 void function_options::test_and_set_nparams(unsigned n)
 549 {
 550         if (nparams==0) {
 551                 nparams = n;
 552         } else if (nparams!=n) {
 553                 // we do not throw an exception here because this code is
 554                 // usually executed before main(), so the exception could not
 555                 // caught anyhow
 556                 std::cerr << "WARNING: number of parameters ("
 557                           << n << ") differs from number set before ("
 558                           << nparams << ")" << std::endl;
 559         }
 560 }
 561
 562 /** This can be used as a hook for external applications. */
 563 unsigned function::current_serial = 0;
 564
 565
 566 GINAC_IMPLEMENT_REGISTERED_CLASS(function, exprseq)
 567
 568 //////////
 569 // default ctor, dtor, copy ctor, assignment operator and helpers
 570 //////////
 571
 572 // public
 573
 574 function::function() : serial(0)
 575 {
 576         tinfo_key = TINFO_function;
 577 }
 578
 579 // protected
 580
 581 void function::copy(const function & other)
 582 {
 583         inherited::copy(other);
 584         serial = other.serial;
 585 }
 586
 587 void function::destroy(bool call_parent)
 588 {
 589         if (call_parent)
 590                 inherited::destroy(call_parent);
 591 }
 592
 593 //////////
 594 // other ctors
 595 //////////
 596
 597 // public
 598
 599 function::function(unsigned ser) : serial(ser)
 600 {
 601         tinfo_key = TINFO_function;
 602 }
 603
 604 // the following lines have been generated for max. ${maxargs} parameters
 605 $constructors_implementation
 606 // end of generated lines
 607
 608 function::function(unsigned ser, const exprseq & es) : exprseq(es), serial(ser)
 609 {
 610         tinfo_key = TINFO_function;
 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, const 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, const 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_of_type(c, print_tree)) {
 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 (unsigned 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_of_type(c, print_csrc)) {
 686
 687                 // Print function name in lowercase
 688                 std::string lname = registered_functions()[serial].name;
 689                 unsigned num = lname.size();
 690                 for (unsigned 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_of_type(c, print_latex)) {
 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 int function::degree(const ex & s) const
 723 {
 724         return is_equal(ex_to<basic>(s)) ? 1 : 0;
 725 }
 726
 727 int function::ldegree(const ex & s) const
 728 {
 729         return is_equal(ex_to<basic>(s)) ? 1 : 0;
 730 }
 731
 732 ex function::coeff(const ex & s, int n) const
 733 {
 734         if (is_equal(ex_to<basic>(s)))
 735                 return n==1 ? _ex1 : _ex0;
 736         else
 737                 return n==0 ? ex(*this) : _ex0;
 738 }
 739
 740 ex function::eval(int level) const
 741 {
 742         GINAC_ASSERT(serial<registered_functions().size());
 743
 744         if (level>1) {
 745                 // first evaluate children, then we will end up here again
 746                 return function(serial,evalchildren(level));
 747         }
 748
 749         const function_options &opt = registered_functions()[serial];
 750
 751         // Canonicalize argument order according to the symmetry properties
 752         if (seq.size() > 1 && !(opt.symtree.is_zero())) {
 753                 exvector v = seq;
 754                 GINAC_ASSERT(is_a<symmetry>(opt.symtree));
 755                 int sig = canonicalize(v.begin(), ex_to<symmetry>(opt.symtree));
 756                 if (sig != INT_MAX) {
 757                         // Something has changed while sorting arguments, more evaluations later
 758                         if (sig == 0)
 759                                 return _ex0;
 760                         return ex(sig) * thisexprseq(v);
 761                 }
 762         }
 763
 764         if (opt.eval_f==0) {
 765                 return this->hold();
 766         }
 767
 768         bool use_remember = opt.use_remember;
 769         ex eval_result;
 770         if (use_remember && lookup_remember_table(eval_result)) {
 771                 return eval_result;
 772         }
 773         current_serial = serial;
 774         if (registered_functions()[serial].eval_use_exvector_args)
 775                 eval_result = ((eval_funcp_exvector)(registered_functions()[serial].eval_f))(seq);
 776         else
 777         switch (opt.nparams) {
 778                 // the following lines have been generated for max. ${maxargs} parameters
 779 ${eval_switch_statement}
 780                 // end of generated lines
 781         default:
 782                 throw(std::logic_error("function::eval(): invalid nparams"));
 783         }
 784         if (use_remember) {
 785                 store_remember_table(eval_result);
 786         }
 787         return eval_result;
 788 }
 789
 790 ex function::evalf(int level) const
 791 {
 792         GINAC_ASSERT(serial<registered_functions().size());
 793
 794         // Evaluate children first
 795         exvector eseq;
 796         if (level == 1)
 797                 eseq = seq;
 798         else if (level == -max_recursion_level)
 799                 throw(std::runtime_error("max recursion level reached"));
 800         else
 801                 eseq.reserve(seq.size());
 802         --level;
 803         exvector::const_iterator it = seq.begin(), itend = seq.end();
 804         while (it != itend) {
 805                 eseq.push_back(it->evalf(level));
 806                 ++it;
 807         }
 808
 809         if (registered_functions()[serial].evalf_f==0) {
 810                 return function(serial,eseq).hold();
 811         }
 812         current_serial = serial;
 813         if (registered_functions()[serial].evalf_use_exvector_args)
 814                 return ((evalf_funcp_exvector)(registered_functions()[serial].evalf_f))(seq);
 815         switch (registered_functions()[serial].nparams) {
 816                 // the following lines have been generated for max. ${maxargs} parameters
 817 ${evalf_switch_statement}
 818                 // end of generated lines
 819         }
 820         throw(std::logic_error("function::evalf(): invalid nparams"));
 821 }
 822
 823 unsigned function::calchash(void) const
 824 {
 825         unsigned v = golden_ratio_hash(golden_ratio_hash(tinfo()) ^ serial);
 826         for (unsigned i=0; i<nops(); i++) {
 827                 v = rotate_left_31(v);
 828                 v ^= this->op(i).gethash();
 829         }
 830         v &= 0x7FFFFFFFU;
 831         if (flags & status_flags::evaluated) {
 832                 setflag(status_flags::hash_calculated);
 833                 hashvalue = v;
 834         }
 835         return v;
 836 }
 837
 838 ex function::thisexprseq(const exvector & v) const
 839 {
 840         return function(serial,v);
 841 }
 842
 843 ex function::thisexprseq(exvector * vp) const
 844 {
 845         return function(serial,vp);
 846 }
 847
 848 /** Implementation of ex::series for functions.
 849  *  \@see ex::series */
 850 ex function::series(const relational & r, int order, unsigned options) const
 851 {
 852         GINAC_ASSERT(serial<registered_functions().size());
 853
 854         if (registered_functions()[serial].series_f==0) {
 855                 return basic::series(r, order);
 856         }
 857         ex res;
 858         current_serial = serial;
 859         if (registered_functions()[serial].series_use_exvector_args) {
 860                 try {
 861                         res = ((series_funcp_exvector)(registered_functions()[serial].series_f))(seq, r, order, options);
 862                 } catch (do_taylor) {
 863                         res = basic::series(r, order, options);
 864                 }
 865                 return res;
 866         }
 867         switch (registered_functions()[serial].nparams) {
 868                 // the following lines have been generated for max. ${maxargs} parameters
 869 ${series_switch_statement}
 870                 // end of generated lines
 871         }
 872         throw(std::logic_error("function::series(): invalid nparams"));
 873 }
 874
 875 // protected
 876
 877 /** Implementation of ex::diff() for functions. It applies the chain rule,
 878  *  except for the Order term function.
 879  *  \@see ex::diff */
 880 ex function::derivative(const symbol & s) const
 881 {
 882         ex result;
 883
 884         if (serial == function_index_Order) {
 885                 // Order Term function only differentiates the argument
 886                 return Order(seq[0].diff(s));
 887         } else {
 888                 // Chain rule
 889                 ex arg_diff;
 890                 unsigned num = seq.size();
 891                 for (unsigned i=0; i<num; i++) {
 892                         arg_diff = seq[i].diff(s);
 893                         // We apply the chain rule only when it makes sense.  This is not
 894                         // just for performance reasons but also to allow functions to
 895                         // throw when differentiated with respect to one of its arguments
 896                         // without running into trouble with our automatic full
 897                         // differentiation:
 898                         if (!arg_diff.is_zero())
 899                                 result += pderivative(i)*arg_diff;
 900                 }
 901         }
 902         return result;
 903 }
 904
 905 int function::compare_same_type(const basic & other) const
 906 {
 907         GINAC_ASSERT(is_of_type(other, function));
 908         const function & o = static_cast<const function &>(other);
 909
 910         if (serial != o.serial)
 911                 return serial < o.serial ? -1 : 1;
 912         else
 913                 return exprseq::compare_same_type(o);
 914 }
 915
 916 bool function::is_equal_same_type(const basic & other) const
 917 {
 918         GINAC_ASSERT(is_of_type(other, function));
 919         const function & o = static_cast<const function &>(other);
 920
 921         if (serial != o.serial)
 922                 return false;
 923         else
 924                 return exprseq::is_equal_same_type(o);
 925 }
 926
 927 bool function::match_same_type(const basic & other) const
 928 {
 929         GINAC_ASSERT(is_of_type(other, function));
 930         const function & o = static_cast<const function &>(other);
 931
 932         return serial == o.serial;
 933 }
 934
 935 unsigned function::return_type(void) const
 936 {
 937         if (seq.empty())
 938                 return return_types::commutative;
 939         else
 940                 return seq.begin()->return_type();
 941 }
 942
 943 unsigned function::return_type_tinfo(void) const
 944 {
 945         if (seq.empty())
 946                 return tinfo_key;
 947         else
 948                 return seq.begin()->return_type_tinfo();
 949 }
 950
 951 //////////
 952 // new virtual functions which can be overridden by derived classes
 953 //////////
 954
 955 // none
 956
 957 //////////
 958 // non-virtual functions in this class
 959 //////////
 960
 961 // protected
 962
 963 ex function::pderivative(unsigned diff_param) const // partial differentiation
 964 {
 965         GINAC_ASSERT(serial<registered_functions().size());
 966
 967         // No derivative defined? Then return abstract derivative object
 968         if (registered_functions()[serial].derivative_f == NULL)
 969                 return fderivative(serial, diff_param, seq);
 970
 971         current_serial = serial;
 972         if (registered_functions()[serial].derivative_use_exvector_args)
 973                 return ((derivative_funcp_exvector)(registered_functions()[serial].derivative_f))(seq, diff_param);
 974         switch (registered_functions()[serial].nparams) {
 975                 // the following lines have been generated for max. ${maxargs} parameters
 976 ${diff_switch_statement}
 977                 // end of generated lines
 978         }
 979         throw(std::logic_error("function::pderivative(): no diff function defined"));
 980 }
 981
 982 std::vector<function_options> & function::registered_functions(void)
 983 {
 984         static std::vector<function_options> * rf = new std::vector<function_options>;
 985         return *rf;
 986 }
 987
 988 bool function::lookup_remember_table(ex & result) const
 989 {
 990         return remember_table::remember_tables()[serial].lookup_entry(*this,result);
 991 }
 992
 993 void function::store_remember_table(ex const & result) const
 994 {
 995         remember_table::remember_tables()[serial].add_entry(*this,result);
 996 }
 997
 998 // public
 999
1000 unsigned function::register_new(function_options const & opt)
1001 {
1002         unsigned same_name = 0;
1003         for (unsigned i=0; i<registered_functions().size(); ++i) {
1004                 if (registered_functions()[i].name==opt.name) {
1005                         ++same_name;
1006                 }
1007         }
1008         if (same_name>=opt.functions_with_same_name) {
1009                 // we do not throw an exception here because this code is
1010                 // usually executed before main(), so the exception could not
1011                 // caught anyhow
1012                 std::cerr << "WARNING: function name " << opt.name
1013                           << " already in use!" << std::endl;
1014         }
1015         registered_functions().push_back(opt);
1016         if (opt.use_remember) {
1017                 remember_table::remember_tables().
1018                         push_back(remember_table(opt.remember_size,
1019                                                  opt.remember_assoc_size,
1020                                                  opt.remember_strategy));
1021         } else {
1022                 remember_table::remember_tables().push_back(remember_table());
1023         }
1024         return registered_functions().size()-1;
1025 }
1026
1027 /** Find serial number of function by name and number of parameters.
1028  *  Throws exception if function was not found. */
1029 unsigned function::find_function(const std::string &name, unsigned nparams)
1030 {
1031         std::vector<function_options>::const_iterator i = function::registered_functions().begin(), end = function::registered_functions().end();
1032         unsigned serial = 0;
1033         while (i != end) {
1034                 if (i->get_name() == name && i->get_nparams() == nparams)
1035                         return serial;
1036                 ++i;
1037                 ++serial;
1038         }
1039         throw (std::runtime_error("no function '" + name + "' with " + ToString(nparams) + " parameters defined"));
1040 }
1041
1042 /** Return the print name of the function. */
1043 std::string function::get_name(void) const
1044 {
1045         GINAC_ASSERT(serial<registered_functions().size());
1046         return registered_functions()[serial].name;
1047 }
1048
1049 } // namespace GiNaC
1050
1051 END_OF_IMPLEMENTATION
1052
1053 print "Creating interface file function.h...";
1054 open OUT,">function.h" or die "cannot open function.h";
1055 print OUT $interface;
1056 close OUT;
1057 print "ok.\n";
1058
1059 print "Creating implementation file function.cpp...";
1060 open OUT,">function.cpp" or die "cannot open function.cpp";
1061 print OUT $implementation;
1062 close OUT;
1063 print "ok.\n";
1064
1065 print "done.\n";