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 // The TYPECHECK-macros were used inside the _evalf() functions.  They are
 204 // considered obsolete now:  (FIXME: remove them)
 205
 206 #define BEGIN_TYPECHECK \\
 207 bool automatic_typecheck=true;
 208
 209 #define TYPECHECK(VAR,TYPE) \\
 210 if (!is_exactly_a<TYPE>(VAR)) { \\
 211         automatic_typecheck=false; \\
 212 } else
 213
 214 #define TYPECHECK_INTEGER(VAR) \\
 215 if (!(VAR).info(GiNaC::info_flags::integer)) { \\
 216         automatic_typecheck=false; \\
 217 } else
 218
 219 #define END_TYPECHECK(RV) \\
 220 {} \\
 221 if (!automatic_typecheck) { \\
 222         return RV.hold(); \\
 223 }
 224
 225 namespace GiNaC {
 226
 227 class function;
 228 class symmetry;
 229
 230 typedef ex (* eval_funcp)();
 231 typedef ex (* evalf_funcp)();
 232 typedef ex (* derivative_funcp)();
 233 typedef ex (* series_funcp)();
 234
 235 // the following lines have been generated for max. ${maxargs} parameters
 236 $typedef_eval_funcp
 237 $typedef_evalf_funcp
 238 $typedef_derivative_funcp
 239 $typedef_series_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
 249 class function_options
 250 {
 251         friend class function;
 252         friend class fderivative;
 253 public:
 254         function_options();
 255         function_options(std::string const & n, std::string const & tn=std::string());
 256         ~function_options();
 257         void initialize(void);
 258         function_options & set_name(std::string const & n, std::string const & tn=std::string());
 259         function_options & latex_name(std::string const & tn);
 260 // the following lines have been generated for max. ${maxargs} parameters
 261 $eval_func_interface
 262 $evalf_func_interface
 263 $derivative_func_interface
 264 $series_func_interface
 265 // end of generated lines
 266         function_options & eval_func(eval_funcp_exvector e);
 267         function_options & evalf_func(evalf_funcp_exvector ef);
 268         function_options & derivative_func(derivative_funcp_exvector d);
 269         function_options & series_func(series_funcp_exvector s);
 270
 271         function_options & set_return_type(unsigned rt, unsigned rtt=0);
 272         function_options & do_not_evalf_params(void);
 273         function_options & remember(unsigned size, unsigned assoc_size=0,
 274                                     unsigned strategy=remember_strategies::delete_never);
 275         function_options & overloaded(unsigned o);
 276         function_options & set_symmetry(const symmetry & s);
 277         void test_and_set_nparams(unsigned n);
 278         std::string get_name(void) const { return name; }
 279         unsigned get_nparams(void) const { return nparams; }
 280         bool has_derivative(void) const { return derivative_f != NULL; }
 281
 282 protected:
 283         std::string name;
 284         std::string TeX_name;
 285
 286         unsigned nparams;
 287
 288         eval_funcp eval_f;
 289         evalf_funcp evalf_f;
 290         derivative_funcp derivative_f;
 291         series_funcp series_f;
 292
 293         bool evalf_params_first;
 294
 295         bool use_return_type;
 296         unsigned return_type;
 297         unsigned return_type_tinfo;
 298
 299         bool use_remember;
 300         unsigned remember_size;
 301         unsigned remember_assoc_size;
 302         unsigned remember_strategy;
 303
 304         bool eval_use_exvector_args;
 305         bool evalf_use_exvector_args;
 306         bool derivative_use_exvector_args;
 307         bool series_use_exvector_args;
 308
 309         unsigned functions_with_same_name;
 310
 311         ex symtree;
 312 };
 313
 314 /** The class function is used to implement builtin functions like sin, cos...
 315         and user defined functions */
 316 class function : public exprseq
 317 {
 318         GINAC_DECLARE_REGISTERED_CLASS(function, exprseq)
 319
 320         // CINT has a linking problem
 321 #ifndef __MAKECINT__
 322         friend void ginsh_get_ginac_functions(void);
 323 #endif // def __MAKECINT__
 324
 325         friend class remember_table_entry;
 326         // friend class remember_table_list;
 327         // friend class remember_table;
 328
 329 // member functions
 330
 331         // other ctors
 332 public:
 333         function(unsigned ser);
 334         // the following lines have been generated for max. ${maxargs} parameters
 335 $constructors_interface
 336         // end of generated lines
 337         function(unsigned ser, const exprseq & es);
 338         function(unsigned ser, const exvector & v, bool discardable = false);
 339         function(unsigned ser, exvector * vp); // vp will be deleted
 340
 341         // functions overriding virtual functions from base classes
 342 public:
 343         void print(const print_context & c, unsigned level = 0) const;
 344         unsigned precedence(void) const {return 70;}
 345         int degree(const ex & s) const;
 346         int ldegree(const ex & s) const;
 347         ex coeff(const ex & s, int n = 1) const;
 348         ex expand(unsigned options=0) const;
 349         ex eval(int level=0) const;
 350         ex evalf(int level=0) const;
 351         unsigned calchash(void) const;
 352         ex series(const relational & r, int order, unsigned options = 0) const;
 353         ex thisexprseq(const exvector & v) const;
 354         ex thisexprseq(exvector * vp) const;
 355 protected:
 356         ex derivative(const symbol & s) const;
 357         bool is_equal_same_type(const basic & other) const;
 358         bool match_same_type(const basic & other) const;
 359         unsigned return_type(void) const;
 360         unsigned return_type_tinfo(void) const;
 361
 362         // new virtual functions which can be overridden by derived classes
 363         // none
 364
 365         // non-virtual functions in this class
 366 protected:
 367         ex pderivative(unsigned diff_param) const; // partial differentiation
 368         static std::vector<function_options> & registered_functions(void);
 369         bool lookup_remember_table(ex & result) const;
 370         void store_remember_table(ex const & result) const;
 371 public:
 372         static unsigned register_new(function_options const & opt);
 373         static unsigned current_serial;
 374         static unsigned find_function(const std::string &name, unsigned nparams);
 375         unsigned get_serial(void) const {return serial;}
 376         std::string get_name(void) const;
 377
 378 // member variables
 379
 380 protected:
 381         unsigned serial;
 382 };
 383
 384 // utility functions/macros
 385
 386 /** Specialization of is_exactly_a<function>(obj) for objects of type function. */
 387 template<> inline bool is_exactly_a<function>(const basic & obj)
 388 {
 389         return obj.tinfo()==TINFO_function;
 390 }
 391
 392 #define is_ex_the_function(OBJ, FUNCNAME) \\
 393         (is_exactly_a<GiNaC::function>(OBJ) && ex_to<GiNaC::function>(OBJ).get_serial() == function_index_##FUNCNAME)
 394
 395 } // namespace GiNaC
 396
 397 #endif // ndef __GINAC_FUNCTION_H__
 398
 399 END_OF_INTERFACE
 400
 401 $implementation=<<END_OF_IMPLEMENTATION;
 402 /** \@file function.cpp
 403  *
 404  *  Implementation of class of symbolic functions. */
 405
 406 /*
 407  *  This file was generated automatically by function.pl.
 408  *  Please do not modify it directly, edit the perl script instead!
 409  *  function.pl options: \$maxargs=${maxargs}
 410  *
 411  *  GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
 412  *
 413  *  This program is free software; you can redistribute it and/or modify
 414  *  it under the terms of the GNU General Public License as published by
 415  *  the Free Software Foundation; either version 2 of the License, or
 416  *  (at your option) any later version.
 417  *
 418  *  This program is distributed in the hope that it will be useful,
 419  *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 420  *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 421  *  GNU General Public License for more details.
 422  *
 423  *  You should have received a copy of the GNU General Public License
 424  *  along with this program; if not, write to the Free Software
 425  *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 426  */
 427
 428 #include <string>
 429 #include <stdexcept>
 430 #include <list>
 431
 432 #include "function.h"
 433 #include "fderivative.h"
 434 #include "ex.h"
 435 #include "lst.h"
 436 #include "symmetry.h"
 437 #include "print.h"
 438 #include "archive.h"
 439 #include "inifcns.h"
 440 #include "tostring.h"
 441 #include "utils.h"
 442 #include "remember.h"
 443
 444 namespace GiNaC {
 445
 446 //////////
 447 // helper class function_options
 448 //////////
 449
 450 function_options::function_options()
 451 {
 452         initialize();
 453 }
 454
 455 function_options::function_options(std::string const & n, std::string const & tn)
 456 {
 457         initialize();
 458         set_name(n,tn);
 459 }
 460
 461 function_options::~function_options()
 462 {
 463         // nothing to clean up at the moment
 464 }
 465
 466 void function_options::initialize(void)
 467 {
 468         set_name("unnamed_function","\\\\mbox{unnamed}");
 469         nparams = 0;
 470         eval_f = evalf_f = derivative_f = series_f = 0;
 471         evalf_params_first = true;
 472         use_return_type = false;
 473         eval_use_exvector_args = false;
 474         evalf_use_exvector_args = false;
 475         derivative_use_exvector_args = false;
 476         series_use_exvector_args = false;
 477         use_remember = false;
 478         functions_with_same_name = 1;
 479         symtree = 0;
 480 }
 481
 482 function_options & function_options::set_name(std::string const & n,
 483                                               std::string const & tn)
 484 {
 485         name = n;
 486         if (tn==std::string())
 487                 TeX_name = "\\\\mbox{"+name+"}";
 488         else
 489                 TeX_name = tn;
 490         return *this;
 491 }
 492
 493 function_options & function_options::latex_name(std::string const & tn)
 494 {
 495         TeX_name = tn;
 496         return *this;
 497 }
 498
 499 // the following lines have been generated for max. ${maxargs} parameters
 500 $eval_func_implementation
 501 $evalf_func_implementation
 502 $derivative_func_implementation
 503 $series_func_implementation
 504 // end of generated lines
 505
 506 function_options& function_options::eval_func(eval_funcp_exvector e)
 507 {
 508         eval_use_exvector_args = true;
 509         eval_f = eval_funcp(e);
 510         return *this;
 511 }
 512 function_options& function_options::evalf_func(evalf_funcp_exvector ef)
 513 {
 514         evalf_use_exvector_args = true;
 515         evalf_f = evalf_funcp(ef);
 516         return *this;
 517 }
 518 function_options& function_options::derivative_func(derivative_funcp_exvector d)
 519 {
 520         derivative_use_exvector_args = true;
 521         derivative_f = derivative_funcp(d);
 522         return *this;
 523 }
 524 function_options& function_options::series_func(series_funcp_exvector s)
 525 {
 526         series_use_exvector_args = true;
 527         series_f = series_funcp(s);
 528         return *this;
 529 }
 530
 531
 532 function_options & function_options::set_return_type(unsigned rt, unsigned rtt)
 533 {
 534         use_return_type = true;
 535         return_type = rt;
 536         return_type_tinfo = rtt;
 537         return *this;
 538 }
 539
 540 function_options & function_options::do_not_evalf_params(void)
 541 {
 542         evalf_params_first = false;
 543         return *this;
 544 }
 545
 546 function_options & function_options::remember(unsigned size,
 547                                               unsigned assoc_size,
 548                                               unsigned strategy)
 549 {
 550         use_remember = true;
 551         remember_size = size;
 552         remember_assoc_size = assoc_size;
 553         remember_strategy = strategy;
 554         return *this;
 555 }
 556
 557 function_options & function_options::overloaded(unsigned o)
 558 {
 559         functions_with_same_name = o;
 560         return *this;
 561 }
 562
 563 function_options & function_options::set_symmetry(const symmetry & s)
 564 {
 565         symtree = s;
 566         return *this;
 567 }
 568
 569 void function_options::test_and_set_nparams(unsigned n)
 570 {
 571         if (nparams==0) {
 572                 nparams = n;
 573         } else if (nparams!=n) {
 574                 // we do not throw an exception here because this code is
 575                 // usually executed before main(), so the exception could not
 576                 // caught anyhow
 577                 std::cerr << "WARNING: number of parameters ("
 578                           << n << ") differs from number set before ("
 579                           << nparams << ")" << std::endl;
 580         }
 581 }
 582
 583 /** This can be used as a hook for external applications. */
 584 unsigned function::current_serial = 0;
 585
 586
 587 GINAC_IMPLEMENT_REGISTERED_CLASS(function, exprseq)
 588
 589 //////////
 590 // default ctor, dtor, copy ctor, assignment operator and helpers
 591 //////////
 592
 593 // public
 594
 595 function::function() : serial(0)
 596 {
 597         tinfo_key = TINFO_function;
 598 }
 599
 600 // protected
 601
 602 void function::copy(const function & other)
 603 {
 604         inherited::copy(other);
 605         serial = other.serial;
 606 }
 607
 608 void function::destroy(bool call_parent)
 609 {
 610         if (call_parent)
 611                 inherited::destroy(call_parent);
 612 }
 613
 614 //////////
 615 // other ctors
 616 //////////
 617
 618 // public
 619
 620 function::function(unsigned ser) : serial(ser)
 621 {
 622         tinfo_key = TINFO_function;
 623 }
 624
 625 // the following lines have been generated for max. ${maxargs} parameters
 626 $constructors_implementation
 627 // end of generated lines
 628
 629 function::function(unsigned ser, const exprseq & es) : exprseq(es), serial(ser)
 630 {
 631         tinfo_key = TINFO_function;
 632 }
 633
 634 function::function(unsigned ser, const exvector & v, bool discardable)
 635   : exprseq(v,discardable), serial(ser)
 636 {
 637         tinfo_key = TINFO_function;
 638 }
 639
 640 function::function(unsigned ser, exvector * vp)
 641   : exprseq(vp), serial(ser)
 642 {
 643         tinfo_key = TINFO_function;
 644 }
 645
 646 //////////
 647 // archiving
 648 //////////
 649
 650 /** Construct object from archive_node. */
 651 function::function(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
 652 {
 653         // Find serial number by function name
 654         std::string s;
 655         if (n.find_string("name", s)) {
 656                 unsigned int ser = 0;
 657                 std::vector<function_options>::const_iterator i = registered_functions().begin(), iend = registered_functions().end();
 658                 while (i != iend) {
 659                         if (s == i->name) {
 660                                 serial = ser;
 661                                 return;
 662                         }
 663                         ++i; ++ser;
 664                 }
 665                 throw (std::runtime_error("unknown function '" + s + "' in archive"));
 666         } else
 667                 throw (std::runtime_error("unnamed function in archive"));
 668 }
 669
 670 /** Unarchive the object. */
 671 ex function::unarchive(const archive_node &n, const lst &sym_lst)
 672 {
 673         return (new function(n, sym_lst))->setflag(status_flags::dynallocated);
 674 }
 675
 676 /** Archive the object. */
 677 void function::archive(archive_node &n) const
 678 {
 679         inherited::archive(n);
 680         GINAC_ASSERT(serial < registered_functions().size());
 681         n.add_string("name", registered_functions()[serial].name);
 682 }
 683
 684 //////////
 685 // functions overriding virtual functions from base classes
 686 //////////
 687
 688 // public
 689
 690 void function::print(const print_context & c, unsigned level) const
 691 {
 692         GINAC_ASSERT(serial<registered_functions().size());
 693
 694         if (is_of_type(c, print_tree)) {
 695
 696                 c.s << std::string(level, ' ') << class_name() << " "
 697                     << registered_functions()[serial].name
 698                     << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
 699                     << ", nops=" << nops()
 700                     << std::endl;
 701                 unsigned delta_indent = static_cast<const print_tree &>(c).delta_indent;
 702                 for (unsigned i=0; i<seq.size(); ++i)
 703                         seq[i].print(c, level + delta_indent);
 704                 c.s << std::string(level + delta_indent, ' ') << "=====" << std::endl;
 705
 706         } else if (is_of_type(c, print_csrc)) {
 707
 708                 // Print function name in lowercase
 709                 std::string lname = registered_functions()[serial].name;
 710                 unsigned num = lname.size();
 711                 for (unsigned i=0; i<num; i++)
 712                         lname[i] = tolower(lname[i]);
 713                 c.s << lname << "(";
 714
 715                 // Print arguments, separated by commas
 716                 exvector::const_iterator it = seq.begin(), itend = seq.end();
 717                 while (it != itend) {
 718                         it->print(c);
 719                         ++it;
 720                         if (it != itend)
 721                                 c.s << ",";
 722                 }
 723                 c.s << ")";
 724
 725         } else if (is_of_type(c, print_latex)) {
 726                 c.s << registered_functions()[serial].TeX_name;
 727                 printseq(c, '(', ',', ')', exprseq::precedence(), function::precedence());
 728         } else {
 729                 c.s << registered_functions()[serial].name;
 730                 printseq(c, '(', ',', ')', exprseq::precedence(), function::precedence());
 731         }
 732 }
 733
 734 ex function::expand(unsigned options) const
 735 {
 736         // Only expand arguments when asked to do so
 737         if (options & expand_options::expand_function_args)
 738                 return inherited::expand(options);
 739         else
 740                 return (options == 0) ? setflag(status_flags::expanded) : *this;
 741 }
 742
 743 int function::degree(const ex & s) const
 744 {
 745         return is_equal(ex_to<basic>(s)) ? 1 : 0;
 746 }
 747
 748 int function::ldegree(const ex & s) const
 749 {
 750         return is_equal(ex_to<basic>(s)) ? 1 : 0;
 751 }
 752
 753 ex function::coeff(const ex & s, int n) const
 754 {
 755         if (is_equal(ex_to<basic>(s)))
 756                 return n==1 ? _ex1 : _ex0;
 757         else
 758                 return n==0 ? ex(*this) : _ex0;
 759 }
 760
 761 ex function::eval(int level) const
 762 {
 763         GINAC_ASSERT(serial<registered_functions().size());
 764
 765         if (level>1) {
 766                 // first evaluate children, then we will end up here again
 767                 return function(serial,evalchildren(level));
 768         }
 769
 770         const function_options &opt = registered_functions()[serial];
 771
 772         // Canonicalize argument order according to the symmetry properties
 773         if (seq.size() > 1 && !(opt.symtree.is_zero())) {
 774                 exvector v = seq;
 775                 GINAC_ASSERT(is_a<symmetry>(opt.symtree));
 776                 int sig = canonicalize(v.begin(), ex_to<symmetry>(opt.symtree));
 777                 if (sig != INT_MAX) {
 778                         // Something has changed while sorting arguments, more evaluations later
 779                         if (sig == 0)
 780                                 return _ex0;
 781                         return ex(sig) * thisexprseq(v);
 782                 }
 783         }
 784
 785         if (opt.eval_f==0) {
 786                 return this->hold();
 787         }
 788
 789         bool use_remember = opt.use_remember;
 790         ex eval_result;
 791         if (use_remember && lookup_remember_table(eval_result)) {
 792                 return eval_result;
 793         }
 794         current_serial = serial;
 795         if (registered_functions()[serial].eval_use_exvector_args)
 796                 eval_result = ((eval_funcp_exvector)(registered_functions()[serial].eval_f))(seq);
 797         else
 798         switch (opt.nparams) {
 799                 // the following lines have been generated for max. ${maxargs} parameters
 800 ${eval_switch_statement}
 801                 // end of generated lines
 802         default:
 803                 throw(std::logic_error("function::eval(): invalid nparams"));
 804         }
 805         if (use_remember) {
 806                 store_remember_table(eval_result);
 807         }
 808         return eval_result;
 809 }
 810
 811 ex function::evalf(int level) const
 812 {
 813         GINAC_ASSERT(serial<registered_functions().size());
 814
 815         // Evaluate children first
 816         exvector eseq;
 817         if (level == 1)
 818                 eseq = seq;
 819         else if (level == -max_recursion_level)
 820                 throw(std::runtime_error("max recursion level reached"));
 821         else
 822                 eseq.reserve(seq.size());
 823         --level;
 824         exvector::const_iterator it = seq.begin(), itend = seq.end();
 825         while (it != itend) {
 826                 eseq.push_back(it->evalf(level));
 827                 ++it;
 828         }
 829
 830         if (registered_functions()[serial].evalf_f==0) {
 831                 return function(serial,eseq).hold();
 832         }
 833         current_serial = serial;
 834         if (registered_functions()[serial].evalf_use_exvector_args)
 835                 return ((evalf_funcp_exvector)(registered_functions()[serial].evalf_f))(seq);
 836         switch (registered_functions()[serial].nparams) {
 837                 // the following lines have been generated for max. ${maxargs} parameters
 838 ${evalf_switch_statement}
 839                 // end of generated lines
 840         }
 841         throw(std::logic_error("function::evalf(): invalid nparams"));
 842 }
 843
 844 unsigned function::calchash(void) const
 845 {
 846         unsigned v = golden_ratio_hash(golden_ratio_hash(tinfo()) ^ serial);
 847         for (unsigned i=0; i<nops(); i++) {
 848                 v = rotate_left_31(v);
 849                 v ^= this->op(i).gethash();
 850         }
 851         v &= 0x7FFFFFFFU;
 852         if (flags & status_flags::evaluated) {
 853                 setflag(status_flags::hash_calculated);
 854                 hashvalue = v;
 855         }
 856         return v;
 857 }
 858
 859 ex function::thisexprseq(const exvector & v) const
 860 {
 861         return function(serial,v);
 862 }
 863
 864 ex function::thisexprseq(exvector * vp) const
 865 {
 866         return function(serial,vp);
 867 }
 868
 869 /** Implementation of ex::series for functions.
 870  *  \@see ex::series */
 871 ex function::series(const relational & r, int order, unsigned options) const
 872 {
 873         GINAC_ASSERT(serial<registered_functions().size());
 874
 875         if (registered_functions()[serial].series_f==0) {
 876                 return basic::series(r, order);
 877         }
 878         ex res;
 879         current_serial = serial;
 880         if (registered_functions()[serial].series_use_exvector_args) {
 881                 try {
 882                         res = ((series_funcp_exvector)(registered_functions()[serial].series_f))(seq, r, order, options);
 883                 } catch (do_taylor) {
 884                         res = basic::series(r, order, options);
 885                 }
 886                 return res;
 887         }
 888         switch (registered_functions()[serial].nparams) {
 889                 // the following lines have been generated for max. ${maxargs} parameters
 890 ${series_switch_statement}
 891                 // end of generated lines
 892         }
 893         throw(std::logic_error("function::series(): invalid nparams"));
 894 }
 895
 896 // protected
 897
 898 /** Implementation of ex::diff() for functions. It applies the chain rule,
 899  *  except for the Order term function.
 900  *  \@see ex::diff */
 901 ex function::derivative(const symbol & s) const
 902 {
 903         ex result;
 904
 905         if (serial == function_index_Order) {
 906                 // Order Term function only differentiates the argument
 907                 return Order(seq[0].diff(s));
 908         } else {
 909                 // Chain rule
 910                 ex arg_diff;
 911                 unsigned num = seq.size();
 912                 for (unsigned i=0; i<num; i++) {
 913                         arg_diff = seq[i].diff(s);
 914                         // We apply the chain rule only when it makes sense.  This is not
 915                         // just for performance reasons but also to allow functions to
 916                         // throw when differentiated with respect to one of its arguments
 917                         // without running into trouble with our automatic full
 918                         // differentiation:
 919                         if (!arg_diff.is_zero())
 920                                 result += pderivative(i)*arg_diff;
 921                 }
 922         }
 923         return result;
 924 }
 925
 926 int function::compare_same_type(const basic & other) const
 927 {
 928         GINAC_ASSERT(is_of_type(other, function));
 929         const function & o = static_cast<const function &>(other);
 930
 931         if (serial != o.serial)
 932                 return serial < o.serial ? -1 : 1;
 933         else
 934                 return exprseq::compare_same_type(o);
 935 }
 936
 937 bool function::is_equal_same_type(const basic & other) const
 938 {
 939         GINAC_ASSERT(is_of_type(other, function));
 940         const function & o = static_cast<const function &>(other);
 941
 942         if (serial != o.serial)
 943                 return false;
 944         else
 945                 return exprseq::is_equal_same_type(o);
 946 }
 947
 948 bool function::match_same_type(const basic & other) const
 949 {
 950         GINAC_ASSERT(is_of_type(other, function));
 951         const function & o = static_cast<const function &>(other);
 952
 953         return serial == o.serial;
 954 }
 955
 956 unsigned function::return_type(void) const
 957 {
 958         if (seq.empty())
 959                 return return_types::commutative;
 960         else
 961                 return seq.begin()->return_type();
 962 }
 963
 964 unsigned function::return_type_tinfo(void) const
 965 {
 966         if (seq.empty())
 967                 return tinfo_key;
 968         else
 969                 return seq.begin()->return_type_tinfo();
 970 }
 971
 972 //////////
 973 // new virtual functions which can be overridden by derived classes
 974 //////////
 975
 976 // none
 977
 978 //////////
 979 // non-virtual functions in this class
 980 //////////
 981
 982 // protected
 983
 984 ex function::pderivative(unsigned diff_param) const // partial differentiation
 985 {
 986         GINAC_ASSERT(serial<registered_functions().size());
 987
 988         // No derivative defined? Then return abstract derivative object
 989         if (registered_functions()[serial].derivative_f == NULL)
 990                 return fderivative(serial, diff_param, seq);
 991
 992         current_serial = serial;
 993         if (registered_functions()[serial].derivative_use_exvector_args)
 994                 return ((derivative_funcp_exvector)(registered_functions()[serial].derivative_f))(seq, diff_param);
 995         switch (registered_functions()[serial].nparams) {
 996                 // the following lines have been generated for max. ${maxargs} parameters
 997 ${diff_switch_statement}
 998                 // end of generated lines
 999         }
1000         throw(std::logic_error("function::pderivative(): no diff function defined"));
1001 }
1002
1003 std::vector<function_options> & function::registered_functions(void)
1004 {
1005         static std::vector<function_options> * rf = new std::vector<function_options>;
1006         return *rf;
1007 }
1008
1009 bool function::lookup_remember_table(ex & result) const
1010 {
1011         return remember_table::remember_tables()[serial].lookup_entry(*this,result);
1012 }
1013
1014 void function::store_remember_table(ex const & result) const
1015 {
1016         remember_table::remember_tables()[serial].add_entry(*this,result);
1017 }
1018
1019 // public
1020
1021 unsigned function::register_new(function_options const & opt)
1022 {
1023         unsigned same_name = 0;
1024         for (unsigned i=0; i<registered_functions().size(); ++i) {
1025                 if (registered_functions()[i].name==opt.name) {
1026                         ++same_name;
1027                 }
1028         }
1029         if (same_name>=opt.functions_with_same_name) {
1030                 // we do not throw an exception here because this code is
1031                 // usually executed before main(), so the exception could not
1032                 // caught anyhow
1033                 std::cerr << "WARNING: function name " << opt.name
1034                           << " already in use!" << std::endl;
1035         }
1036         registered_functions().push_back(opt);
1037         if (opt.use_remember) {
1038                 remember_table::remember_tables().
1039                         push_back(remember_table(opt.remember_size,
1040                                                  opt.remember_assoc_size,
1041                                                  opt.remember_strategy));
1042         } else {
1043                 remember_table::remember_tables().push_back(remember_table());
1044         }
1045         return registered_functions().size()-1;
1046 }
1047
1048 /** Find serial number of function by name and number of parameters.
1049  *  Throws exception if function was not found. */
1050 unsigned function::find_function(const std::string &name, unsigned nparams)
1051 {
1052         std::vector<function_options>::const_iterator i = function::registered_functions().begin(), end = function::registered_functions().end();
1053         unsigned serial = 0;
1054         while (i != end) {
1055                 if (i->get_name() == name && i->get_nparams() == nparams)
1056                         return serial;
1057                 ++i;
1058                 ++serial;
1059         }
1060         throw (std::runtime_error("no function '" + name + "' with " + ToString(nparams) + " parameters defined"));
1061 }
1062
1063 /** Return the print name of the function. */
1064 std::string function::get_name(void) const
1065 {
1066         GINAC_ASSERT(serial<registered_functions().size());
1067         return registered_functions()[serial].name;
1068 }
1069
1070 } // namespace GiNaC
1071
1072 END_OF_IMPLEMENTATION
1073
1074 print "Creating interface file function.h...";
1075 open OUT,">function.h" or die "cannot open function.h";
1076 print OUT $interface;
1077 close OUT;
1078 print "ok.\n";
1079
1080 print "Creating implementation file function.cpp...";
1081 open OUT,">function.cpp" or die "cannot open function.cpp";
1082 print OUT $implementation;
1083 close OUT;
1084 print "ok.\n";
1085
1086 print "done.\n";