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         int degree(const ex & s) const;
 341         int ldegree(const ex & s) const;
 342         ex coeff(const ex & s, int n = 1) const;
 343         ex expand(unsigned options=0) const;
 344         ex eval(int level=0) const;
 345         ex evalf(int level=0) const;
 346         unsigned calchash(void) const;
 347         ex series(const relational & r, int order, unsigned options = 0) const;
 348         ex thisexprseq(const exvector & v) const;
 349         ex thisexprseq(exvector * vp) const;
 350 protected:
 351         ex derivative(const symbol & s) const;
 352         bool is_equal_same_type(const basic & other) const;
 353         unsigned return_type(void) const;
 354         unsigned return_type_tinfo(void) const;
 355
 356         // new virtual functions which can be overridden by derived classes
 357         // none
 358
 359         // non-virtual functions in this class
 360 protected:
 361         ex pderivative(unsigned diff_param) const; // partial differentiation
 362         static std::vector<function_options> & registered_functions(void);
 363         bool lookup_remember_table(ex & result) const;
 364         void store_remember_table(ex const & result) const;
 365 public:
 366         static unsigned register_new(function_options const & opt);
 367         static unsigned find_function(const std::string &name, unsigned nparams);
 368         unsigned getserial(void) const {return serial;}
 369
 370 // member variables
 371
 372 protected:
 373         unsigned serial;
 374 };
 375
 376 // utility functions/macros
 377 inline const function &ex_to_function(const ex &e)
 378 {
 379         return static_cast<const function &>(*e.bp);
 380 }
 381
 382 #define is_ex_the_function(OBJ, FUNCNAME) \\
 383         (is_ex_exactly_of_type(OBJ, function) && static_cast<GiNaC::function *>(OBJ.bp)->getserial() == function_index_##FUNCNAME)
 384
 385 // global constants
 386
 387 extern const function some_function;
 388 extern const std::type_info & typeid_function;
 389
 390 } // namespace GiNaC
 391
 392 #endif // ndef __GINAC_FUNCTION_H__
 393
 394 END_OF_INTERFACE
 395
 396 $implementation=<<END_OF_IMPLEMENTATION;
 397 /** \@file function.cpp
 398  *
 399  *  Implementation of class function. */
 400
 401 /*
 402  *  This file was generated automatically by function.pl.
 403  *  Please do not modify it directly, edit the perl script instead!
 404  *  function.pl options: \$maxargs=${maxargs}
 405  *
 406  *  GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
 407  *
 408  *  This program is free software; you can redistribute it and/or modify
 409  *  it under the terms of the GNU General Public License as published by
 410  *  the Free Software Foundation; either version 2 of the License, or
 411  *  (at your option) any later version.
 412  *
 413  *  This program is distributed in the hope that it will be useful,
 414  *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 415  *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 416  *  GNU General Public License for more details.
 417  *
 418  *  You should have received a copy of the GNU General Public License
 419  *  along with this program; if not, write to the Free Software
 420  *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 421  */
 422
 423 #include <string>
 424 #include <stdexcept>
 425 #include <list>
 426
 427 #include "function.h"
 428 #include "ex.h"
 429 #include "lst.h"
 430 #include "archive.h"
 431 #include "inifcns.h"
 432 #include "utils.h"
 433 #include "debugmsg.h"
 434 #include "remember.h"
 435
 436 namespace GiNaC {
 437
 438 //////////
 439 // helper class function_options
 440 //////////
 441
 442 function_options::function_options()
 443 {
 444         initialize();
 445 }
 446
 447 function_options::function_options(std::string const & n, std::string const & tn)
 448 {
 449         initialize();
 450         set_name(n,tn);
 451 }
 452
 453 function_options::~function_options()
 454 {
 455         // nothing to clean up at the moment
 456 }
 457
 458 void function_options::initialize(void)
 459 {
 460         set_name("unnamed_function","\\\\operatorname{unnamed}");
 461         nparams=0;
 462         eval_f=evalf_f=derivative_f=series_f=0;
 463         evalf_params_first=true;
 464         use_return_type=false;
 465         use_remember=false;
 466         functions_with_same_name=1;
 467 }
 468
 469 function_options & function_options::set_name(std::string const & n,
 470                                               std::string const & tn)
 471 {
 472         name=n;
 473         if (tn==std::string()) {
 474                 TeX_name="\\\\operatorname{"+name+"}";
 475         } else {
 476                 TeX_name=tn;
 477         }
 478         return *this;
 479 }
 480
 481 // the following lines have been generated for max. ${maxargs} parameters
 482 $eval_func_implementation
 483 $evalf_func_implementation
 484 $derivative_func_implementation
 485 $series_func_implementation
 486 // end of generated lines
 487
 488 function_options & function_options::set_return_type(unsigned rt, unsigned rtt)
 489 {
 490         use_return_type=true;
 491         return_type=rt;
 492         return_type_tinfo=rtt;
 493         return *this;
 494 }
 495
 496 function_options & function_options::do_not_evalf_params(void)
 497 {
 498         evalf_params_first=false;
 499         return *this;
 500 }
 501
 502 function_options & function_options::remember(unsigned size,
 503                                               unsigned assoc_size,
 504                                               unsigned strategy)
 505 {
 506         use_remember=true;
 507         remember_size=size;
 508         remember_assoc_size=assoc_size;
 509         remember_strategy=strategy;
 510         return *this;
 511 }
 512
 513 function_options & function_options::overloaded(unsigned o)
 514 {
 515         functions_with_same_name=o;
 516         return *this;
 517 }
 518
 519 void function_options::test_and_set_nparams(unsigned n)
 520 {
 521         if (nparams==0) {
 522                 nparams=n;
 523         } else if (nparams!=n) {
 524                 // we do not throw an exception here because this code is
 525                 // usually executed before main(), so the exception could not
 526                 // caught anyhow
 527                 std::cerr << "WARNING: number of parameters ("
 528                           << n << ") differs from number set before ("
 529                           << nparams << ")" << std::endl;
 530         }
 531 }
 532
 533 GINAC_IMPLEMENT_REGISTERED_CLASS(function, exprseq)
 534
 535 //////////
 536 // default ctor, dtor, copy ctor assignment operator and helpers
 537 //////////
 538
 539 // public
 540
 541 function::function() : serial(0)
 542 {
 543         debugmsg("function default ctor",LOGLEVEL_CONSTRUCT);
 544         tinfo_key = TINFO_function;
 545 }
 546
 547 // protected
 548
 549 void function::copy(const function & other)
 550 {
 551         exprseq::copy(other);
 552         serial=other.serial;
 553 }
 554
 555 void function::destroy(bool call_parent)
 556 {
 557         if (call_parent) exprseq::destroy(call_parent);
 558 }
 559
 560 //////////
 561 // other ctors
 562 //////////
 563
 564 // public
 565
 566 function::function(unsigned ser) : serial(ser)
 567 {
 568         debugmsg("function ctor from unsigned",LOGLEVEL_CONSTRUCT);
 569         tinfo_key = TINFO_function;
 570 }
 571
 572 // the following lines have been generated for max. ${maxargs} parameters
 573 $constructors_implementation
 574 // end of generated lines
 575
 576 function::function(unsigned ser, const exprseq & es) : exprseq(es), serial(ser)
 577 {
 578         debugmsg("function ctor from unsigned,exprseq",LOGLEVEL_CONSTRUCT);
 579         tinfo_key = TINFO_function;
 580 }
 581
 582 function::function(unsigned ser, const exvector & v, bool discardable)
 583   : exprseq(v,discardable), serial(ser)
 584 {
 585         debugmsg("function ctor from string,exvector,bool",LOGLEVEL_CONSTRUCT);
 586         tinfo_key = TINFO_function;
 587 }
 588
 589 function::function(unsigned ser, exvector * vp)
 590   : exprseq(vp), serial(ser)
 591 {
 592         debugmsg("function ctor from unsigned,exvector *",LOGLEVEL_CONSTRUCT);
 593         tinfo_key = TINFO_function;
 594 }
 595
 596 //////////
 597 // archiving
 598 //////////
 599
 600 /** Construct object from archive_node. */
 601 function::function(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
 602 {
 603         debugmsg("function ctor from archive_node", LOGLEVEL_CONSTRUCT);
 604
 605         // Find serial number by function name
 606         std::string s;
 607         if (n.find_string("name", s)) {
 608                 unsigned int ser = 0;
 609                 std::vector<function_options>::const_iterator i = registered_functions().begin(), iend = registered_functions().end();
 610                 while (i != iend) {
 611                         if (s == i->name) {
 612                                 serial = ser;
 613                                 return;
 614                         }
 615                         i++; ser++;
 616                 }
 617                 throw (std::runtime_error("unknown function '" + s + "' in archive"));
 618         } else
 619                 throw (std::runtime_error("unnamed function in archive"));
 620 }
 621
 622 /** Unarchive the object. */
 623 ex function::unarchive(const archive_node &n, const lst &sym_lst)
 624 {
 625         return (new function(n, sym_lst))->setflag(status_flags::dynallocated);
 626 }
 627
 628 /** Archive the object. */
 629 void function::archive(archive_node &n) const
 630 {
 631         inherited::archive(n);
 632         GINAC_ASSERT(serial < registered_functions().size());
 633         n.add_string("name", registered_functions()[serial].name);
 634 }
 635
 636 //////////
 637 // functions overriding virtual functions from bases classes
 638 //////////
 639
 640 // public
 641
 642 void function::printraw(std::ostream & os) const
 643 {
 644         debugmsg("function printraw",LOGLEVEL_PRINT);
 645
 646         GINAC_ASSERT(serial<registered_functions().size());
 647
 648         os << class_name() << "(name=" << registered_functions()[serial].name;
 649         for (exvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
 650                 os << ",";
 651                 (*it).bp->print(os);
 652         }
 653         os << ")";
 654 }
 655
 656 void function::print(std::ostream & os, unsigned upper_precedence) const
 657 {
 658         debugmsg("function print",LOGLEVEL_PRINT);
 659
 660         GINAC_ASSERT(serial<registered_functions().size());
 661
 662         os << registered_functions()[serial].name;
 663         printseq(os,'(',',',')',exprseq::precedence,function::precedence);
 664 }
 665
 666 void function::printtree(std::ostream & os, unsigned indent) const
 667 {
 668         debugmsg("function printtree",LOGLEVEL_PRINT);
 669
 670         GINAC_ASSERT(serial<registered_functions().size());
 671
 672         os << std::string(indent,' ') << class_name() << " "
 673            << registered_functions()[serial].name
 674            << ", hash=" << hashvalue
 675            << " (0x" << std::hex << hashvalue << std::dec << ")"
 676            << ", flags=" << flags
 677            << ", nops=" << nops() << std::endl;
 678         for (unsigned i=0; i<nops(); ++i) {
 679                 seq[i].printtree(os,indent+delta_indent);
 680         }
 681         os << std::string(indent+delta_indent,' ') << "=====" << std::endl;
 682 }
 683
 684 void function::printcsrc(std::ostream & os, unsigned type, unsigned upper_precedence) const
 685 {
 686         debugmsg("function print csrc",LOGLEVEL_PRINT);
 687
 688         GINAC_ASSERT(serial<registered_functions().size());
 689
 690         // Print function name in lowercase
 691         std::string lname;
 692         lname=registered_functions()[serial].name;
 693         for (unsigned i=0; i<lname.size(); i++)
 694                 lname[i] = tolower(lname[i]);
 695         os << lname << "(";
 696
 697         // Print arguments, separated by commas
 698         exvector::const_iterator it = seq.begin();
 699         exvector::const_iterator itend = seq.end();
 700         while (it != itend) {
 701                 it->bp->printcsrc(os, type, 0);
 702                 it++;
 703                 if (it != itend)
 704                         os << ",";
 705         }
 706         os << ")";
 707 }
 708
 709 ex function::expand(unsigned options) const
 710 {
 711         return this->setflag(status_flags::expanded);
 712 }
 713
 714 int function::degree(const ex & s) const
 715 {
 716         return is_equal(*s.bp) ? 1 : 0;
 717 }
 718
 719 int function::ldegree(const ex & s) const
 720 {
 721         return is_equal(*s.bp) ? 1 : 0;
 722 }
 723
 724 ex function::coeff(const ex & s, int n) const
 725 {
 726         if (is_equal(*s.bp))
 727                 return n==1 ? _ex1() : _ex0();
 728         else
 729                 return n==0 ? ex(*this) : _ex0();
 730 }
 731
 732 ex function::eval(int level) const
 733 {
 734         GINAC_ASSERT(serial<registered_functions().size());
 735
 736         if (level>1) {
 737                 // first evaluate children, then we will end up here again
 738                 return function(serial,evalchildren(level));
 739         }
 740
 741         if (registered_functions()[serial].eval_f==0) {
 742                 return this->hold();
 743         }
 744
 745         bool use_remember=registered_functions()[serial].use_remember;
 746         ex eval_result;
 747         if (use_remember && lookup_remember_table(eval_result)) {
 748                 return eval_result;
 749         }
 750
 751         switch (registered_functions()[serial].nparams) {
 752                 // the following lines have been generated for max. ${maxargs} parameters
 753 ${eval_switch_statement}
 754                 // end of generated lines
 755         default:
 756                 throw(std::logic_error("function::eval(): invalid nparams"));
 757         }
 758         if (use_remember) {
 759                 store_remember_table(eval_result);
 760         }
 761         return eval_result;
 762 }
 763
 764 ex function::evalf(int level) const
 765 {
 766         GINAC_ASSERT(serial<registered_functions().size());
 767
 768         exvector eseq=evalfchildren(level);
 769
 770         if (registered_functions()[serial].evalf_f==0) {
 771                 return function(serial,eseq).hold();
 772         }
 773         switch (registered_functions()[serial].nparams) {
 774                 // the following lines have been generated for max. ${maxargs} parameters
 775 ${evalf_switch_statement}
 776                 // end of generated lines
 777         }
 778         throw(std::logic_error("function::evalf(): invalid nparams"));
 779 }
 780
 781 unsigned function::calchash(void) const
 782 {
 783         unsigned v = golden_ratio_hash(golden_ratio_hash(tinfo()) ^ serial);
 784         for (unsigned i=0; i<nops(); i++) {
 785                 v = rotate_left_31(v);
 786                 v ^= this->op(i).gethash();
 787         }
 788         v &= 0x7FFFFFFFU;
 789         if (flags & status_flags::evaluated) {
 790                 setflag(status_flags::hash_calculated);
 791                 hashvalue = v;
 792         }
 793         return v;
 794 }
 795
 796 ex function::thisexprseq(const exvector & v) const
 797 {
 798         return function(serial,v);
 799 }
 800
 801 ex function::thisexprseq(exvector * vp) const
 802 {
 803         return function(serial,vp);
 804 }
 805
 806 /** Implementation of ex::series for functions.
 807  *  \@see ex::series */
 808 ex function::series(const relational & r, int order, unsigned options) const
 809 {
 810         GINAC_ASSERT(serial<registered_functions().size());
 811
 812         if (registered_functions()[serial].series_f==0) {
 813                 return basic::series(r, order);
 814         }
 815         ex res;
 816         switch (registered_functions()[serial].nparams) {
 817                 // the following lines have been generated for max. ${maxargs} parameters
 818 ${series_switch_statement}
 819                 // end of generated lines
 820         }
 821         throw(std::logic_error("function::series(): invalid nparams"));
 822 }
 823
 824 // protected
 825
 826
 827 /** Implementation of ex::diff() for functions. It applies the chain rule,
 828  *  except for the Order term function.
 829  *  \@see ex::diff */
 830 ex function::derivative(const symbol & s) const
 831 {
 832         ex result;
 833
 834         if (serial == function_index_Order) {
 835                 // Order Term function only differentiates the argument
 836                 return Order(seq[0].diff(s));
 837         } else if (serial == function_index_Derivative) {
 838                 // Inert derivative performs chain rule on the first argument only, and
 839                 // adds differentiation parameter to list (second argument)
 840                 GINAC_ASSERT(is_ex_exactly_of_type(seq[0], function));
 841                 GINAC_ASSERT(is_ex_exactly_of_type(seq[1], function));
 842                 ex fcn = seq[0];
 843                 ex arg_diff;
 844                 for (unsigned i=0; i!=fcn.nops(); i++) {
 845                         arg_diff = fcn.op(i).diff(s);
 846                         if (!arg_diff.is_zero()) {
 847                                 lst new_lst = ex_to_lst(seq[1]);
 848                                 new_lst.append(i);
 849                                 result += arg_diff * Derivative(fcn, new_lst);
 850                         }
 851                 }
 852         } else {
 853                 // Chain rule
 854                 ex arg_diff;
 855                 for (unsigned i=0; i!=seq.size(); i++) {
 856                         arg_diff = seq[i].diff(s);
 857                         // We apply the chain rule only when it makes sense.  This is not
 858                         // just for performance reasons but also to allow functions to
 859                         // throw when differentiated with respect to one of its arguments
 860                         // without running into trouble with our automatic full
 861                         // differentiation:
 862                         if (!arg_diff.is_zero())
 863                                 result += pderivative(i)*arg_diff;
 864                 }
 865         }
 866         return result;
 867 }
 868
 869 int function::compare_same_type(const basic & other) const
 870 {
 871         GINAC_ASSERT(is_of_type(other, function));
 872         const function & o=static_cast<function &>(const_cast<basic &>(other));
 873
 874         if (serial!=o.serial) {
 875                 return serial < o.serial ? -1 : 1;
 876         }
 877         return exprseq::compare_same_type(o);
 878 }
 879
 880 bool function::is_equal_same_type(const basic & other) const
 881 {
 882         GINAC_ASSERT(is_of_type(other, function));
 883         const function & o=static_cast<function &>(const_cast<basic &>(other));
 884
 885         if (serial!=o.serial) return false;
 886         return exprseq::is_equal_same_type(o);
 887 }
 888
 889 unsigned function::return_type(void) const
 890 {
 891         if (seq.size()==0) {
 892                 return return_types::commutative;
 893         }
 894         return (*seq.begin()).return_type();
 895 }
 896
 897 unsigned function::return_type_tinfo(void) const
 898 {
 899         if (seq.size()==0) {
 900                 return tinfo_key;
 901         }
 902         return (*seq.begin()).return_type_tinfo();
 903 }
 904
 905 //////////
 906 // new virtual functions which can be overridden by derived classes
 907 //////////
 908
 909 // none
 910
 911 //////////
 912 // non-virtual functions in this class
 913 //////////
 914
 915 // protected
 916
 917 ex function::pderivative(unsigned diff_param) const // partial differentiation
 918 {
 919         GINAC_ASSERT(serial<registered_functions().size());
 920
 921         if (registered_functions()[serial].derivative_f==0) {
 922                 return Derivative(*this, lst(ex(diff_param)));
 923         }
 924         switch (registered_functions()[serial].nparams) {
 925                 // the following lines have been generated for max. ${maxargs} parameters
 926 ${diff_switch_statement}
 927                 // end of generated lines
 928         }
 929         throw(std::logic_error("function::pderivative(): no diff function defined"));
 930 }
 931
 932 std::vector<function_options> & function::registered_functions(void)
 933 {
 934         static std::vector<function_options> * rf = new std::vector<function_options>;
 935         return *rf;
 936 }
 937
 938 bool function::lookup_remember_table(ex & result) const
 939 {
 940         return remember_table::remember_tables()[serial].lookup_entry(*this,result);
 941 }
 942
 943 void function::store_remember_table(ex const & result) const
 944 {
 945         remember_table::remember_tables()[serial].add_entry(*this,result);
 946 }
 947
 948 // public
 949
 950 unsigned function::register_new(function_options const & opt)
 951 {
 952         unsigned same_name=0;
 953         for (unsigned i=0; i<registered_functions().size(); ++i) {
 954                 if (registered_functions()[i].name==opt.name) {
 955                         same_name++;
 956                 }
 957         }
 958         if (same_name>=opt.functions_with_same_name) {
 959                 // we do not throw an exception here because this code is
 960                 // usually executed before main(), so the exception could not
 961                 // caught anyhow
 962                 std::cerr << "WARNING: function name " << opt.name
 963                                   << " already in use!" << std::endl;
 964         }
 965         registered_functions().push_back(opt);
 966         if (opt.use_remember) {
 967                 remember_table::remember_tables().
 968                         push_back(remember_table(opt.remember_size,
 969                                                                          opt.remember_assoc_size,
 970                                                                          opt.remember_strategy));
 971         } else {
 972                 remember_table::remember_tables().push_back(remember_table());
 973         }
 974         return registered_functions().size()-1;
 975 }
 976
 977 /** Find serial number of function by name and number of parameters.
 978  *  Throws exception if function was not found. */
 979 unsigned function::find_function(const std::string &name, unsigned nparams)
 980 {
 981         std::vector<function_options>::const_iterator i = function::registered_functions().begin(), end = function::registered_functions().end();
 982         unsigned serial = 0;
 983         while (i != end) {
 984                 if (i->get_name() == name && i->get_nparams() == nparams)
 985                         return serial;
 986                 i++;
 987                 serial++;
 988         }
 989         throw (std::runtime_error("no function '" + name + "' with " + ToString(nparams) + " parameters defined"));
 990 }
 991
 992 //////////
 993 // static member variables
 994 //////////
 995
 996 // none
 997
 998 //////////
 999 // global constants
1000 //////////
1001
1002 const function some_function;
1003 const std::type_info & typeid_function=typeid(some_function);
1004
1005 } // namespace GiNaC
1006
1007 END_OF_IMPLEMENTATION
1008
1009 print "Creating interface file function.h...";
1010 open OUT,">function.h" or die "cannot open function.h";
1011 print OUT $interface;
1012 close OUT;
1013 print "ok.\n";
1014
1015 print "Creating implementation file function.cpp...";
1016 open OUT,">function.cpp" or die "cannot open function.cpp";
1017 print OUT $implementation;
1018 close OUT;
1019 print "ok.\n";
1020
1021 print "done.\n";