ginac/function.pl

   1 $maxargs=13;
   2
   3 sub generate_seq {
   4         my ($seq_template,$n)=@_;
   5         my ($res,$N);
   6
   7         $res='';
   8         for ($N=1; $N<=$n; $N++) {
   9                 $res .= eval('"' . $seq_template . '"');
  10                 if ($N!=$n) {
  11                         $res .= ', ';
  12                 }
  13         }
  14         return $res;
  15 }
  16
  17 sub generate_from_to {
  18         my ($template,$seq_template1,$seq_template2,$from,$to)=@_;
  19         my ($res,$N,$SEQ);
  20
  21         $res='';
  22         for ($N=$from; $N<=$to; $N++) {
  23                 $SEQ1=generate_seq($seq_template1,$N);
  24                 $SEQ2=generate_seq($seq_template2,$N);
  25                 $res .= eval('"' . $template . '"');
  26                 $SEQ1=''; # to avoid main::SEQ1 used only once warning
  27                 $SEQ2=''; # same as above
  28         }
  29         return $res;
  30 }
  31
  32 sub generate {
  33         my ($template,$seq_template1,$seq_template2)=@_;
  34         return generate_from_to($template,$seq_template1,$seq_template2,1,$maxargs);
  35 }
  36
  37 $declare_function_macro = <<'END_OF_DECLARE_FUNCTION_1_AND_2P_MACRO';
  38 #define DECLARE_FUNCTION_1P(NAME) \
  39 extern const unsigned function_index_##NAME; \
  40 inline GiNaC::function NAME(const GiNaC::ex & p1) { \
  41         return GiNaC::function(function_index_##NAME, p1); \
  42 }
  43 #define DECLARE_FUNCTION_2P(NAME) \
  44 extern const unsigned function_index_##NAME; \
  45 inline GiNaC::function NAME(const GiNaC::ex & p1, const GiNaC::ex & p2) { \
  46         return GiNaC::function(function_index_##NAME, p1, p2); \
  47 }
  48
  49 END_OF_DECLARE_FUNCTION_1_AND_2P_MACRO
  50
  51 $declare_function_macro .= generate_from_to(
  52         <<'END_OF_DECLARE_FUNCTION_MACRO','const GiNaC::ex & p${N}','p${N}',3,$maxargs);
  53 #define DECLARE_FUNCTION_${N}P(NAME) \\
  54 extern const unsigned function_index_##NAME; \\
  55 inline GiNaC::function NAME(${SEQ1}) { \\
  56         return GiNaC::function(function_index_##NAME, ${SEQ2}); \\
  57 }
  58
  59 END_OF_DECLARE_FUNCTION_MACRO
  60
  61 $typedef_eval_funcp=generate(
  62 'typedef ex (* eval_funcp_${N})(${SEQ1});'."\n",
  63 'const ex &','');
  64
  65 $typedef_evalf_funcp=generate(
  66 'typedef ex (* evalf_funcp_${N})(${SEQ1});'."\n",
  67 'const ex &','');
  68
  69 $typedef_derivative_funcp=generate(
  70 'typedef ex (* derivative_funcp_${N})(${SEQ1}, unsigned);'."\n",
  71 'const ex &','');
  72
  73 $typedef_series_funcp=generate(
  74 'typedef ex (* series_funcp_${N})(${SEQ1}, const relational &, int, unsigned);'."\n",
  75 'const ex &','');
  76
  77 $eval_func_interface=generate('    function_options & eval_func(eval_funcp_${N} e);'."\n",'','');
  78
  79 $evalf_func_interface=generate('    function_options & evalf_func(evalf_funcp_${N} ef);'."\n",'','');
  80
  81 $derivative_func_interface=generate('    function_options & derivative_func(derivative_funcp_${N} d);'."\n",'','');
  82
  83 $series_func_interface=generate('    function_options & series_func(series_funcp_${N} s);'."\n",'','');
  84
  85 $constructors_interface=generate(
  86 '    function(unsigned ser, ${SEQ1});'."\n",
  87 'const ex & param${N}','');
  88
  89 $constructors_implementation=generate(
  90         <<'END_OF_CONSTRUCTORS_IMPLEMENTATION','const ex & param${N}','param${N}');
  91 function::function(unsigned ser, ${SEQ1})
  92         : exprseq(${SEQ2}), serial(ser)
  93 {
  94         debugmsg(\"function ctor from unsigned,${N}*ex\",LOGLEVEL_CONSTRUCT);
  95         tinfo_key = TINFO_function;
  96 }
  97 END_OF_CONSTRUCTORS_IMPLEMENTATION
  98
  99 $eval_switch_statement=generate(
 100         <<'END_OF_EVAL_SWITCH_STATEMENT','seq[${N}-1]','');
 101         case ${N}:
 102                 eval_result=((eval_funcp_${N})(registered_functions()[serial].eval_f))(${SEQ1});
 103                 break;
 104 END_OF_EVAL_SWITCH_STATEMENT
 105
 106 $evalf_switch_statement=generate(
 107         <<'END_OF_EVALF_SWITCH_STATEMENT','eseq[${N}-1]','');
 108         case ${N}:
 109                 return ((evalf_funcp_${N})(registered_functions()[serial].evalf_f))(${SEQ1});
 110 END_OF_EVALF_SWITCH_STATEMENT
 111
 112 $diff_switch_statement=generate(
 113         <<'END_OF_DIFF_SWITCH_STATEMENT','seq[${N}-1]','');
 114         case ${N}:
 115                 return ((derivative_funcp_${N})(registered_functions()[serial].derivative_f))(${SEQ1},diff_param);
 116 END_OF_DIFF_SWITCH_STATEMENT
 117
 118 $series_switch_statement=generate(
 119         <<'END_OF_SERIES_SWITCH_STATEMENT','seq[${N}-1]','');
 120         case ${N}:
 121                 try {
 122                         res = ((series_funcp_${N})(registered_functions()[serial].series_f))(${SEQ1},r,order,options);
 123                 } catch (do_taylor) {
 124                         res = basic::series(r, order, options);
 125                 }
 126                 return res;
 127 END_OF_SERIES_SWITCH_STATEMENT
 128
 129 $eval_func_implementation=generate(
 130         <<'END_OF_EVAL_FUNC_IMPLEMENTATION','','');
 131 function_options & function_options::eval_func(eval_funcp_${N} e)
 132 {
 133         test_and_set_nparams(${N});
 134         eval_f=eval_funcp(e);
 135         return *this;
 136 }
 137 END_OF_EVAL_FUNC_IMPLEMENTATION
 138
 139 $evalf_func_implementation=generate(
 140         <<'END_OF_EVALF_FUNC_IMPLEMENTATION','','');
 141 function_options & function_options::evalf_func(evalf_funcp_${N} ef)
 142 {
 143         test_and_set_nparams(${N});
 144         evalf_f=evalf_funcp(ef);
 145         return *this;
 146 }
 147 END_OF_EVALF_FUNC_IMPLEMENTATION
 148
 149 $derivative_func_implementation=generate(
 150         <<'END_OF_DERIVATIVE_FUNC_IMPLEMENTATION','','');
 151 function_options & function_options::derivative_func(derivative_funcp_${N} d)
 152 {
 153         test_and_set_nparams(${N});
 154         derivative_f=derivative_funcp(d);
 155         return *this;
 156 }
 157 END_OF_DERIVATIVE_FUNC_IMPLEMENTATION
 158
 159 $series_func_implementation=generate(
 160         <<'END_OF_SERIES_FUNC_IMPLEMENTATION','','');
 161 function_options & function_options::series_func(series_funcp_${N} s)
 162 {
 163         test_and_set_nparams(${N});
 164         series_f=series_funcp(s);
 165         return *this;
 166 }
 167 END_OF_SERIES_FUNC_IMPLEMENTATION
 168
 169 $interface=<<END_OF_INTERFACE;
 170 /** \@file function.h
 171  *
 172  *  Interface to abstract class function (new function concept). */
 173
 174 /*
 175  *  This file was generated automatically by function.pl.
 176  *  Please do not modify it directly, edit the perl script instead!
 177  *  function.pl options: \$maxargs=${maxargs}
 178  *
 179  *  GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
 180  *
 181  *  This program is free software; you can redistribute it and/or modify
 182  *  it under the terms of the GNU General Public License as published by
 183  *  the Free Software Foundation; either version 2 of the License, or
 184  *  (at your option) any later version.
 185  *
 186  *  This program is distributed in the hope that it will be useful,
 187  *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 188  *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 189  *  GNU General Public License for more details.
 190  *
 191  *  You should have received a copy of the GNU General Public License
 192  *  along with this program; if not, write to the Free Software
 193  *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 194  */
 195
 196 #ifndef __GINAC_FUNCTION_H__
 197 #define __GINAC_FUNCTION_H__
 198
 199 #include <string>
 200 #include <vector>
 201
 202 // CINT needs <algorithm> to work properly with <vector>
 203 #include <algorithm>
 204
 205 #include "exprseq.h"
 206
 207 // the following lines have been generated for max. ${maxargs} parameters
 208 $declare_function_macro
 209 // end of generated lines
 210
 211 #define REGISTER_FUNCTION(NAME,OPT) \\
 212 const unsigned function_index_##NAME= \\
 213         GiNaC::function::register_new(GiNaC::function_options(#NAME).OPT);
 214
 215 #define REGISTER_FUNCTION_OLD(NAME,E,EF,D,S) \\
 216 const unsigned function_index_##NAME= \\
 217         GiNaC::function::register_new(GiNaC::function_options(#NAME). \\
 218                                       eval_func(E). \\
 219                                       evalf_func(EF). \\
 220                                       derivative_func(D). \\
 221                                       series_func(S));
 222
 223 #define BEGIN_TYPECHECK \\
 224 bool automatic_typecheck=true;
 225
 226 #define TYPECHECK(VAR,TYPE) \\
 227 if (!is_ex_exactly_of_type(VAR,TYPE)) { \\
 228         automatic_typecheck=false; \\
 229 } else
 230
 231 #define TYPECHECK_INTEGER(VAR) \\
 232 if (!(VAR).info(GiNaC::info_flags::integer)) { \\
 233         automatic_typecheck=false; \\
 234 } else
 235
 236 #define END_TYPECHECK(RV) \\
 237 {} \\
 238 if (!automatic_typecheck) { \\
 239         return RV.hold(); \\
 240 }
 241
 242 namespace GiNaC {
 243
 244 class function;
 245
 246 typedef ex (* eval_funcp)();
 247 typedef ex (* evalf_funcp)();
 248 typedef ex (* derivative_funcp)();
 249 typedef ex (* series_funcp)();
 250
 251 // the following lines have been generated for max. ${maxargs} parameters
 252 $typedef_eval_funcp
 253 $typedef_evalf_funcp
 254 $typedef_derivative_funcp
 255 $typedef_series_funcp
 256 // end of generated lines
 257
 258 class function_options
 259 {
 260         friend class function;
 261 public:
 262         function_options();
 263         function_options(std::string const & n, std::string const & tn=std::string());
 264         ~function_options();
 265         void initialize(void);
 266         function_options & set_name(std::string const & n, std::string const & tn=std::string());
 267 // the following lines have been generated for max. ${maxargs} parameters
 268 $eval_func_interface
 269 $evalf_func_interface
 270 $derivative_func_interface
 271 $series_func_interface
 272 // end of generated lines
 273         function_options & set_return_type(unsigned rt, unsigned rtt=0);
 274         function_options & do_not_evalf_params(void);
 275         function_options & remember(unsigned size, unsigned assoc_size=0,
 276                                     unsigned strategy=remember_strategies::delete_never);
 277         function_options & overloaded(unsigned o);
 278         void test_and_set_nparams(unsigned n);
 279         std::string get_name(void) const { return name; }
 280         unsigned get_nparams(void) const { return nparams; }
 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         unsigned functions_with_same_name;
 305 };
 306
 307 /** The class function is used to implement builtin functions like sin, cos...
 308         and user defined functions */
 309 class function : public exprseq
 310 {
 311         GINAC_DECLARE_REGISTERED_CLASS(function, exprseq)
 312
 313         // CINT has a linking problem
 314 #ifndef __MAKECINT__
 315         friend void ginsh_get_ginac_functions(void);
 316 #endif // def __MAKECINT__
 317
 318         friend class remember_table_entry;
 319         // friend class remember_table_list;
 320         // friend class remember_table;
 321
 322 // member functions
 323
 324         // other ctors
 325 public:
 326         function(unsigned ser);
 327         // the following lines have been generated for max. ${maxargs} parameters
 328 $constructors_interface
 329         // end of generated lines
 330         function(unsigned ser, const exprseq & es);
 331         function(unsigned ser, const exvector & v, bool discardable=0);
 332         function(unsigned ser, exvector * vp); // vp will be deleted
 333
 334         // functions overriding virtual functions from bases classes
 335 public:
 336         void printraw(std::ostream & os) const;
 337         void print(std::ostream & os, unsigned upper_precedence=0) const;
 338         void printtree(std::ostream & os, unsigned indent) const;
 339         void printcsrc(std::ostream & os, unsigned type, unsigned upper_precedence=0) const;
 340         ex expand(unsigned options=0) const;
 341         ex eval(int level=0) const;
 342         ex evalf(int level=0) const;
 343         unsigned calchash(void) const;
 344         ex series(const relational & r, int order, unsigned options = 0) const;
 345         ex thisexprseq(const exvector & v) const;
 346         ex thisexprseq(exvector * vp) const;
 347 protected:
 348         ex derivative(const symbol & s) const;
 349         bool is_equal_same_type(const basic & other) const;
 350         unsigned return_type(void) const;
 351         unsigned return_type_tinfo(void) const;
 352
 353         // new virtual functions which can be overridden by derived classes
 354         // none
 355
 356         // non-virtual functions in this class
 357 protected:
 358         ex pderivative(unsigned diff_param) const; // partial differentiation
 359         static std::vector<function_options> & registered_functions(void);
 360         bool lookup_remember_table(ex & result) const;
 361         void store_remember_table(ex const & result) const;
 362 public:
 363         static unsigned register_new(function_options const & opt);
 364         static unsigned find_function(const std::string &name, unsigned nparams);
 365         unsigned getserial(void) const {return serial;}
 366
 367 // member variables
 368
 369 protected:
 370         unsigned serial;
 371 };
 372
 373 // utility functions/macros
 374 inline const function &ex_to_function(const ex &e)
 375 {
 376         return static_cast<const function &>(*e.bp);
 377 }
 378
 379 #define is_ex_the_function(OBJ, FUNCNAME) \\
 380         (is_ex_exactly_of_type(OBJ, function) && static_cast<GiNaC::function *>(OBJ.bp)->getserial() == function_index_##FUNCNAME)
 381
 382 // global constants
 383
 384 extern const function some_function;
 385 extern const std::type_info & typeid_function;
 386
 387 } // namespace GiNaC
 388
 389 #endif // ndef __GINAC_FUNCTION_H__
 390
 391 END_OF_INTERFACE
 392
 393 $implementation=<<END_OF_IMPLEMENTATION;
 394 /** \@file function.cpp
 395  *
 396  *  Implementation of class function. */
 397
 398 /*
 399  *  This file was generated automatically by function.pl.
 400  *  Please do not modify it directly, edit the perl script instead!
 401  *  function.pl options: \$maxargs=${maxargs}
 402  *
 403  *  GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
 404  *
 405  *  This program is free software; you can redistribute it and/or modify
 406  *  it under the terms of the GNU General Public License as published by
 407  *  the Free Software Foundation; either version 2 of the License, or
 408  *  (at your option) any later version.
 409  *
 410  *  This program is distributed in the hope that it will be useful,
 411  *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 412  *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 413  *  GNU General Public License for more details.
 414  *
 415  *  You should have received a copy of the GNU General Public License
 416  *  along with this program; if not, write to the Free Software
 417  *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 418  */
 419
 420 #include <string>
 421 #include <stdexcept>
 422 #include <list>
 423
 424 #include "function.h"
 425 #include "ex.h"
 426 #include "lst.h"
 427 #include "archive.h"
 428 #include "inifcns.h"
 429 #include "utils.h"
 430 #include "debugmsg.h"
 431 #include "remember.h"
 432
 433 namespace GiNaC {
 434
 435 //////////
 436 // helper class function_options
 437 //////////
 438
 439 function_options::function_options()
 440 {
 441         initialize();
 442 }
 443
 444 function_options::function_options(std::string const & n, std::string const & tn)
 445 {
 446         initialize();
 447         set_name(n,tn);
 448 }
 449
 450 function_options::~function_options()
 451 {
 452         // nothing to clean up at the moment
 453 }
 454
 455 void function_options::initialize(void)
 456 {
 457         set_name("unnamed_function","\\\\operatorname{unnamed}");
 458         nparams=0;
 459         eval_f=evalf_f=derivative_f=series_f=0;
 460         evalf_params_first=true;
 461         use_return_type=false;
 462         use_remember=false;
 463         functions_with_same_name=1;
 464 }
 465
 466 function_options & function_options::set_name(std::string const & n,
 467                                               std::string const & tn)
 468 {
 469         name=n;
 470         if (tn==std::string()) {
 471                 TeX_name="\\\\operatorname{"+name+"}";
 472         } else {
 473                 TeX_name=tn;
 474         }
 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::set_return_type(unsigned rt, unsigned rtt)
 486 {
 487         use_return_type=true;
 488         return_type=rt;
 489         return_type_tinfo=rtt;
 490         return *this;
 491 }
 492
 493 function_options & function_options::do_not_evalf_params(void)
 494 {
 495         evalf_params_first=false;
 496         return *this;
 497 }
 498
 499 function_options & function_options::remember(unsigned size,
 500                                               unsigned assoc_size,
 501                                               unsigned strategy)
 502 {
 503         use_remember=true;
 504         remember_size=size;
 505         remember_assoc_size=assoc_size;
 506         remember_strategy=strategy;
 507         return *this;
 508 }
 509
 510 function_options & function_options::overloaded(unsigned o)
 511 {
 512         functions_with_same_name=o;
 513         return *this;
 514 }
 515
 516 void function_options::test_and_set_nparams(unsigned n)
 517 {
 518         if (nparams==0) {
 519                 nparams=n;
 520         } else if (nparams!=n) {
 521                 // we do not throw an exception here because this code is
 522                 // usually executed before main(), so the exception could not
 523                 // caught anyhow
 524                 std::cerr << "WARNING: number of parameters ("
 525                           << n << ") differs from number set before ("
 526                           << nparams << ")" << std::endl;
 527         }
 528 }
 529
 530 GINAC_IMPLEMENT_REGISTERED_CLASS(function, exprseq)
 531
 532 //////////
 533 // default ctor, dtor, copy ctor assignment operator and helpers
 534 //////////
 535
 536 // public
 537
 538 function::function() : serial(0)
 539 {
 540         debugmsg("function default ctor",LOGLEVEL_CONSTRUCT);
 541         tinfo_key = TINFO_function;
 542 }
 543
 544 // protected
 545
 546 void function::copy(const function & other)
 547 {
 548         exprseq::copy(other);
 549         serial=other.serial;
 550 }
 551
 552 void function::destroy(bool call_parent)
 553 {
 554         if (call_parent) exprseq::destroy(call_parent);
 555 }
 556
 557 //////////
 558 // other ctors
 559 //////////
 560
 561 // public
 562
 563 function::function(unsigned ser) : serial(ser)
 564 {
 565         debugmsg("function ctor from unsigned",LOGLEVEL_CONSTRUCT);
 566         tinfo_key = TINFO_function;
 567 }
 568
 569 // the following lines have been generated for max. ${maxargs} parameters
 570 $constructors_implementation
 571 // end of generated lines
 572
 573 function::function(unsigned ser, const exprseq & es) : exprseq(es), serial(ser)
 574 {
 575         debugmsg("function ctor from unsigned,exprseq",LOGLEVEL_CONSTRUCT);
 576         tinfo_key = TINFO_function;
 577 }
 578
 579 function::function(unsigned ser, const exvector & v, bool discardable)
 580   : exprseq(v,discardable), serial(ser)
 581 {
 582         debugmsg("function ctor from string,exvector,bool",LOGLEVEL_CONSTRUCT);
 583         tinfo_key = TINFO_function;
 584 }
 585
 586 function::function(unsigned ser, exvector * vp)
 587   : exprseq(vp), serial(ser)
 588 {
 589         debugmsg("function ctor from unsigned,exvector *",LOGLEVEL_CONSTRUCT);
 590         tinfo_key = TINFO_function;
 591 }
 592
 593 //////////
 594 // archiving
 595 //////////
 596
 597 /** Construct object from archive_node. */
 598 function::function(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
 599 {
 600         debugmsg("function ctor from archive_node", LOGLEVEL_CONSTRUCT);
 601
 602         // Find serial number by function name
 603         std::string s;
 604         if (n.find_string("name", s)) {
 605                 unsigned int ser = 0;
 606                 std::vector<function_options>::const_iterator i = registered_functions().begin(), iend = registered_functions().end();
 607                 while (i != iend) {
 608                         if (s == i->name) {
 609                                 serial = ser;
 610                                 return;
 611                         }
 612                         i++; ser++;
 613                 }
 614                 throw (std::runtime_error("unknown function '" + s + "' in archive"));
 615         } else
 616                 throw (std::runtime_error("unnamed function in archive"));
 617 }
 618
 619 /** Unarchive the object. */
 620 ex function::unarchive(const archive_node &n, const lst &sym_lst)
 621 {
 622         return (new function(n, sym_lst))->setflag(status_flags::dynallocated);
 623 }
 624
 625 /** Archive the object. */
 626 void function::archive(archive_node &n) const
 627 {
 628         inherited::archive(n);
 629         GINAC_ASSERT(serial < registered_functions().size());
 630         n.add_string("name", registered_functions()[serial].name);
 631 }
 632
 633 //////////
 634 // functions overriding virtual functions from bases classes
 635 //////////
 636
 637 // public
 638
 639 void function::printraw(std::ostream & os) const
 640 {
 641         debugmsg("function printraw",LOGLEVEL_PRINT);
 642
 643         GINAC_ASSERT(serial<registered_functions().size());
 644
 645         os << class_name() << "(name=" << registered_functions()[serial].name;
 646         for (exvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
 647                 os << ",";
 648                 (*it).bp->print(os);
 649         }
 650         os << ")";
 651 }
 652
 653 void function::print(std::ostream & os, unsigned upper_precedence) const
 654 {
 655         debugmsg("function print",LOGLEVEL_PRINT);
 656
 657         GINAC_ASSERT(serial<registered_functions().size());
 658
 659         os << registered_functions()[serial].name;
 660         printseq(os,'(',',',')',exprseq::precedence,function::precedence);
 661 }
 662
 663 void function::printtree(std::ostream & os, unsigned indent) const
 664 {
 665         debugmsg("function printtree",LOGLEVEL_PRINT);
 666
 667         GINAC_ASSERT(serial<registered_functions().size());
 668
 669         os << std::string(indent,' ') << class_name() << " "
 670            << registered_functions()[serial].name
 671            << ", hash=" << hashvalue
 672            << " (0x" << std::hex << hashvalue << std::dec << ")"
 673            << ", flags=" << flags
 674            << ", nops=" << nops() << std::endl;
 675         for (unsigned i=0; i<nops(); ++i) {
 676                 seq[i].printtree(os,indent+delta_indent);
 677         }
 678         os << std::string(indent+delta_indent,' ') << "=====" << std::endl;
 679 }
 680
 681 void function::printcsrc(std::ostream & os, unsigned type, unsigned upper_precedence) const
 682 {
 683         debugmsg("function print csrc",LOGLEVEL_PRINT);
 684
 685         GINAC_ASSERT(serial<registered_functions().size());
 686
 687         // Print function name in lowercase
 688         std::string lname;
 689         lname=registered_functions()[serial].name;
 690         for (unsigned i=0; i<lname.size(); i++)
 691                 lname[i] = tolower(lname[i]);
 692         os << lname << "(";
 693
 694         // Print arguments, separated by commas
 695         exvector::const_iterator it = seq.begin();
 696         exvector::const_iterator itend = seq.end();
 697         while (it != itend) {
 698                 it->bp->printcsrc(os, type, 0);
 699                 it++;
 700                 if (it != itend)
 701                         os << ",";
 702         }
 703         os << ")";
 704 }
 705
 706 ex function::expand(unsigned options) const
 707 {
 708         return this->setflag(status_flags::expanded);
 709 }
 710
 711 ex function::eval(int level) const
 712 {
 713         GINAC_ASSERT(serial<registered_functions().size());
 714
 715         if (level>1) {
 716                 // first evaluate children, then we will end up here again
 717                 return function(serial,evalchildren(level));
 718         }
 719
 720         if (registered_functions()[serial].eval_f==0) {
 721                 return this->hold();
 722         }
 723
 724         bool use_remember=registered_functions()[serial].use_remember;
 725         ex eval_result;
 726         if (use_remember && lookup_remember_table(eval_result)) {
 727                 return eval_result;
 728         }
 729
 730         switch (registered_functions()[serial].nparams) {
 731                 // the following lines have been generated for max. ${maxargs} parameters
 732 ${eval_switch_statement}
 733                 // end of generated lines
 734         default:
 735                 throw(std::logic_error("function::eval(): invalid nparams"));
 736         }
 737         if (use_remember) {
 738                 store_remember_table(eval_result);
 739         }
 740         return eval_result;
 741 }
 742
 743 ex function::evalf(int level) const
 744 {
 745         GINAC_ASSERT(serial<registered_functions().size());
 746
 747         exvector eseq=evalfchildren(level);
 748
 749         if (registered_functions()[serial].evalf_f==0) {
 750                 return function(serial,eseq).hold();
 751         }
 752         switch (registered_functions()[serial].nparams) {
 753                 // the following lines have been generated for max. ${maxargs} parameters
 754 ${evalf_switch_statement}
 755                 // end of generated lines
 756         }
 757         throw(std::logic_error("function::evalf(): invalid nparams"));
 758 }
 759
 760 unsigned function::calchash(void) const
 761 {
 762         unsigned v = golden_ratio_hash(golden_ratio_hash(tinfo()) ^ serial);
 763         for (unsigned i=0; i<nops(); i++) {
 764                 v = rotate_left_31(v);
 765                 v ^= this->op(i).gethash();
 766         }
 767         v &= 0x7FFFFFFFU;
 768         if (flags & status_flags::evaluated) {
 769                 setflag(status_flags::hash_calculated);
 770                 hashvalue = v;
 771         }
 772         return v;
 773 }
 774
 775 ex function::thisexprseq(const exvector & v) const
 776 {
 777         return function(serial,v);
 778 }
 779
 780 ex function::thisexprseq(exvector * vp) const
 781 {
 782         return function(serial,vp);
 783 }
 784
 785 /** Implementation of ex::series for functions.
 786  *  \@see ex::series */
 787 ex function::series(const relational & r, int order, unsigned options) const
 788 {
 789         GINAC_ASSERT(serial<registered_functions().size());
 790
 791         if (registered_functions()[serial].series_f==0) {
 792                 return basic::series(r, order);
 793         }
 794         ex res;
 795         switch (registered_functions()[serial].nparams) {
 796                 // the following lines have been generated for max. ${maxargs} parameters
 797 ${series_switch_statement}
 798                 // end of generated lines
 799         }
 800         throw(std::logic_error("function::series(): invalid nparams"));
 801 }
 802
 803 // protected
 804
 805
 806 /** Implementation of ex::diff() for functions. It applies the chain rule,
 807  *  except for the Order term function.
 808  *  \@see ex::diff */
 809 ex function::derivative(const symbol & s) const
 810 {
 811         ex result;
 812
 813         if (serial == function_index_Order) {
 814                 // Order Term function only differentiates the argument
 815                 return Order(seq[0].diff(s));
 816         } else if (serial == function_index_Derivative) {
 817                 // Inert derivative performs chain rule on the first argument only, and
 818                 // adds differentiation parameter to list (second argument)
 819                 GINAC_ASSERT(is_ex_exactly_of_type(seq[0], function));
 820                 GINAC_ASSERT(is_ex_exactly_of_type(seq[1], function));
 821                 ex fcn = seq[0];
 822                 ex arg_diff;
 823                 for (unsigned i=0; i!=fcn.nops(); i++) {
 824                         arg_diff = fcn.op(i).diff(s);
 825                         if (!arg_diff.is_zero()) {
 826                                 lst new_lst = ex_to_lst(seq[1]);
 827                                 new_lst.append(i);
 828                                 result += arg_diff * Derivative(fcn, new_lst);
 829                         }
 830                 }
 831         } else {
 832                 // Chain rule
 833                 ex arg_diff;
 834                 for (unsigned i=0; i!=seq.size(); i++) {
 835                         arg_diff = seq[i].diff(s);
 836                         // We apply the chain rule only when it makes sense.  This is not
 837                         // just for performance reasons but also to allow functions to
 838                         // throw when differentiated with respect to one of its arguments
 839                         // without running into trouble with our automatic full
 840                         // differentiation:
 841                         if (!arg_diff.is_zero())
 842                                 result += pderivative(i)*arg_diff;
 843                 }
 844         }
 845         return result;
 846 }
 847
 848 int function::compare_same_type(const basic & other) const
 849 {
 850         GINAC_ASSERT(is_of_type(other, function));
 851         const function & o=static_cast<function &>(const_cast<basic &>(other));
 852
 853         if (serial!=o.serial) {
 854                 return serial < o.serial ? -1 : 1;
 855         }
 856         return exprseq::compare_same_type(o);
 857 }
 858
 859 bool function::is_equal_same_type(const basic & other) const
 860 {
 861         GINAC_ASSERT(is_of_type(other, function));
 862         const function & o=static_cast<function &>(const_cast<basic &>(other));
 863
 864         if (serial!=o.serial) return false;
 865         return exprseq::is_equal_same_type(o);
 866 }
 867
 868 unsigned function::return_type(void) const
 869 {
 870         if (seq.size()==0) {
 871                 return return_types::commutative;
 872         }
 873         return (*seq.begin()).return_type();
 874 }
 875
 876 unsigned function::return_type_tinfo(void) const
 877 {
 878         if (seq.size()==0) {
 879                 return tinfo_key;
 880         }
 881         return (*seq.begin()).return_type_tinfo();
 882 }
 883
 884 //////////
 885 // new virtual functions which can be overridden by derived classes
 886 //////////
 887
 888 // none
 889
 890 //////////
 891 // non-virtual functions in this class
 892 //////////
 893
 894 // protected
 895
 896 ex function::pderivative(unsigned diff_param) const // partial differentiation
 897 {
 898         GINAC_ASSERT(serial<registered_functions().size());
 899
 900         if (registered_functions()[serial].derivative_f==0) {
 901                 return Derivative(*this, lst(ex(diff_param)));
 902         }
 903         switch (registered_functions()[serial].nparams) {
 904                 // the following lines have been generated for max. ${maxargs} parameters
 905 ${diff_switch_statement}
 906                 // end of generated lines
 907         }
 908         throw(std::logic_error("function::pderivative(): no diff function defined"));
 909 }
 910
 911 std::vector<function_options> & function::registered_functions(void)
 912 {
 913         static std::vector<function_options> * rf = new std::vector<function_options>;
 914         return *rf;
 915 }
 916
 917 bool function::lookup_remember_table(ex & result) const
 918 {
 919         return remember_table::remember_tables()[serial].lookup_entry(*this,result);
 920 }
 921
 922 void function::store_remember_table(ex const & result) const
 923 {
 924         remember_table::remember_tables()[serial].add_entry(*this,result);
 925 }
 926
 927 // public
 928
 929 unsigned function::register_new(function_options const & opt)
 930 {
 931         unsigned same_name=0;
 932         for (unsigned i=0; i<registered_functions().size(); ++i) {
 933                 if (registered_functions()[i].name==opt.name) {
 934                         same_name++;
 935                 }
 936         }
 937         if (same_name>=opt.functions_with_same_name) {
 938                 // we do not throw an exception here because this code is
 939                 // usually executed before main(), so the exception could not
 940                 // caught anyhow
 941                 std::cerr << "WARNING: function name " << opt.name
 942                                   << " already in use!" << std::endl;
 943         }
 944         registered_functions().push_back(opt);
 945         if (opt.use_remember) {
 946                 remember_table::remember_tables().
 947                         push_back(remember_table(opt.remember_size,
 948                                                                          opt.remember_assoc_size,
 949                                                                          opt.remember_strategy));
 950         } else {
 951                 remember_table::remember_tables().push_back(remember_table());
 952         }
 953         return registered_functions().size()-1;
 954 }
 955
 956 /** Find serial number of function by name and number of parameters.
 957  *  Throws exception if function was not found. */
 958 unsigned function::find_function(const std::string &name, unsigned nparams)
 959 {
 960         std::vector<function_options>::const_iterator i = function::registered_functions().begin(), end = function::registered_functions().end();
 961         unsigned serial = 0;
 962         while (i != end) {
 963                 if (i->get_name() == name && i->get_nparams() == nparams)
 964                         return serial;
 965                 i++;
 966                 serial++;
 967         }
 968         throw (std::runtime_error("no function '" + name + "' with " + ToString(nparams) + " parameters defined"));
 969 }
 970
 971 //////////
 972 // static member variables
 973 //////////
 974
 975 // none
 976
 977 //////////
 978 // global constants
 979 //////////
 980
 981 const function some_function;
 982 const std::type_info & typeid_function=typeid(some_function);
 983
 984 } // namespace GiNaC
 985
 986 END_OF_IMPLEMENTATION
 987
 988 print "Creating interface file function.h...";
 989 open OUT,">function.h" or die "cannot open function.h";
 990 print OUT $interface;
 991 close OUT;
 992 print "ok.\n";
 993
 994 print "Creating implementation file function.cpp...";
 995 open OUT,">function.cpp" or die "cannot open function.cpp";
 996 print OUT $implementation;
 997 close OUT;
 998 print "ok.\n";
 999
1000 print "done.\n";