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_exactly_a<TYPE>(VAR)) { \\
 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 class symmetry;
 246
 247 typedef ex (* eval_funcp)();
 248 typedef ex (* evalf_funcp)();
 249 typedef ex (* derivative_funcp)();
 250 typedef ex (* series_funcp)();
 251
 252 // the following lines have been generated for max. ${maxargs} parameters
 253 $typedef_eval_funcp
 254 $typedef_evalf_funcp
 255 $typedef_derivative_funcp
 256 $typedef_series_funcp
 257 // end of generated lines
 258
 259 class function_options
 260 {
 261         friend class function;
 262 public:
 263         function_options();
 264         function_options(std::string const & n, std::string const & tn=std::string());
 265         ~function_options();
 266         void initialize(void);
 267         function_options & set_name(std::string const & n, std::string const & tn=std::string());
 268         function_options & latex_name(std::string const & tn);
 269 // the following lines have been generated for max. ${maxargs} parameters
 270 $eval_func_interface
 271 $evalf_func_interface
 272 $derivative_func_interface
 273 $series_func_interface
 274 // end of generated lines
 275         function_options & set_return_type(unsigned rt, unsigned rtt=0);
 276         function_options & do_not_evalf_params(void);
 277         function_options & remember(unsigned size, unsigned assoc_size=0,
 278                                     unsigned strategy=remember_strategies::delete_never);
 279         function_options & overloaded(unsigned o);
 280         function_options & set_symmetry(const symmetry & s);
 281         void test_and_set_nparams(unsigned n);
 282         std::string get_name(void) const { return name; }
 283         unsigned get_nparams(void) const { return nparams; }
 284
 285 protected:
 286         std::string name;
 287         std::string TeX_name;
 288
 289         unsigned nparams;
 290
 291         eval_funcp eval_f;
 292         evalf_funcp evalf_f;
 293         derivative_funcp derivative_f;
 294         series_funcp series_f;
 295
 296         bool evalf_params_first;
 297
 298         bool use_return_type;
 299         unsigned return_type;
 300         unsigned return_type_tinfo;
 301
 302         bool use_remember;
 303         unsigned remember_size;
 304         unsigned remember_assoc_size;
 305         unsigned remember_strategy;
 306
 307         unsigned functions_with_same_name;
 308
 309         ex symtree;
 310 };
 311
 312 /** The class function is used to implement builtin functions like sin, cos...
 313         and user defined functions */
 314 class function : public exprseq
 315 {
 316         GINAC_DECLARE_REGISTERED_CLASS(function, exprseq)
 317
 318         // CINT has a linking problem
 319 #ifndef __MAKECINT__
 320         friend void ginsh_get_ginac_functions(void);
 321 #endif // def __MAKECINT__
 322
 323         friend class remember_table_entry;
 324         // friend class remember_table_list;
 325         // friend class remember_table;
 326
 327 // member functions
 328
 329         // other ctors
 330 public:
 331         function(unsigned ser);
 332         // the following lines have been generated for max. ${maxargs} parameters
 333 $constructors_interface
 334         // end of generated lines
 335         function(unsigned ser, const exprseq & es);
 336         function(unsigned ser, const exvector & v, bool discardable=0);
 337         function(unsigned ser, exvector * vp); // vp will be deleted
 338
 339         // functions overriding virtual functions from bases classes
 340 public:
 341         void print(const print_context & c, unsigned level = 0) const;
 342         unsigned precedence(void) const {return 70;}
 343         int degree(const ex & s) const;
 344         int ldegree(const ex & s) const;
 345         ex coeff(const ex & s, int n = 1) const;
 346         ex expand(unsigned options=0) const;
 347         ex eval(int level=0) const;
 348         ex evalf(int level=0) const;
 349         unsigned calchash(void) const;
 350         ex series(const relational & r, int order, unsigned options = 0) const;
 351         bool match(const ex & pattern, lst & repl_lst) const;
 352         ex thisexprseq(const exvector & v) const;
 353         ex thisexprseq(exvector * vp) const;
 354 protected:
 355         ex derivative(const symbol & s) const;
 356         bool is_equal_same_type(const basic & other) const;
 357         unsigned return_type(void) const;
 358         unsigned return_type_tinfo(void) const;
 359
 360         // new virtual functions which can be overridden by derived classes
 361         // none
 362
 363         // non-virtual functions in this class
 364 protected:
 365         ex pderivative(unsigned diff_param) const; // partial differentiation
 366         static std::vector<function_options> & registered_functions(void);
 367         bool lookup_remember_table(ex & result) const;
 368         void store_remember_table(ex const & result) const;
 369 public:
 370         static unsigned register_new(function_options const & opt);
 371         static unsigned find_function(const std::string &name, unsigned nparams);
 372         unsigned get_serial(void) const {return serial;}
 373         std::string get_name(void) const;
 374
 375 // member variables
 376
 377 protected:
 378         unsigned serial;
 379 };
 380
 381 // utility functions/macros
 382 /** Return the object of type function handled by an ex.
 383  *  This is unsafe: you need to check the type first. */
 384 inline const function &ex_to_function(const ex &e)
 385 {
 386         return static_cast<const function &>(*e.bp);
 387 }
 388
 389 /** Specialization of is_exactly_a<function>(obj) for objects of type function. */
 390 template<> inline bool is_exactly_a<function>(const basic & obj)
 391 {
 392         return obj.tinfo()==TINFO_function;
 393 }
 394
 395 #define is_ex_the_function(OBJ, FUNCNAME) \\
 396         (is_ex_exactly_of_type(OBJ, function) && static_cast<GiNaC::function *>(OBJ.bp)->get_serial() == function_index_##FUNCNAME)
 397
 398 } // namespace GiNaC
 399
 400 #endif // ndef __GINAC_FUNCTION_H__
 401
 402 END_OF_INTERFACE
 403
 404 $implementation=<<END_OF_IMPLEMENTATION;
 405 /** \@file function.cpp
 406  *
 407  *  Implementation of class function. */
 408
 409 /*
 410  *  This file was generated automatically by function.pl.
 411  *  Please do not modify it directly, edit the perl script instead!
 412  *  function.pl options: \$maxargs=${maxargs}
 413  *
 414  *  GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
 415  *
 416  *  This program is free software; you can redistribute it and/or modify
 417  *  it under the terms of the GNU General Public License as published by
 418  *  the Free Software Foundation; either version 2 of the License, or
 419  *  (at your option) any later version.
 420  *
 421  *  This program is distributed in the hope that it will be useful,
 422  *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 423  *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 424  *  GNU General Public License for more details.
 425  *
 426  *  You should have received a copy of the GNU General Public License
 427  *  along with this program; if not, write to the Free Software
 428  *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 429  */
 430
 431 #include <string>
 432 #include <stdexcept>
 433 #include <list>
 434
 435 #include "function.h"
 436 #include "ex.h"
 437 #include "lst.h"
 438 #include "symmetry.h"
 439 #include "print.h"
 440 #include "archive.h"
 441 #include "inifcns.h"
 442 #include "utils.h"
 443 #include "debugmsg.h"
 444 #include "remember.h"
 445
 446 namespace GiNaC {
 447
 448 //////////
 449 // helper class function_options
 450 //////////
 451
 452 function_options::function_options()
 453 {
 454         initialize();
 455 }
 456
 457 function_options::function_options(std::string const & n, std::string const & tn)
 458 {
 459         initialize();
 460         set_name(n,tn);
 461 }
 462
 463 function_options::~function_options()
 464 {
 465         // nothing to clean up at the moment
 466 }
 467
 468 void function_options::initialize(void)
 469 {
 470         set_name("unnamed_function","\\\\mbox{unnamed}");
 471         nparams=0;
 472         eval_f=evalf_f=derivative_f=series_f=0;
 473         evalf_params_first=true;
 474         use_return_type=false;
 475         use_remember=false;
 476         functions_with_same_name=1;
 477         symtree = 0;
 478 }
 479
 480 function_options & function_options::set_name(std::string const & n,
 481                                               std::string const & tn)
 482 {
 483         name=n;
 484         if (tn==std::string()) {
 485                 TeX_name="\\\\mbox{"+name+"}";
 486         } else {
 487                 TeX_name=tn;
 488         }
 489         return *this;
 490 }
 491
 492 function_options & function_options::latex_name(std::string const & tn)
 493 {
 494         TeX_name=tn;
 495         return *this;
 496 }
 497
 498 // the following lines have been generated for max. ${maxargs} parameters
 499 $eval_func_implementation
 500 $evalf_func_implementation
 501 $derivative_func_implementation
 502 $series_func_implementation
 503 // end of generated lines
 504
 505 function_options & function_options::set_return_type(unsigned rt, unsigned rtt)
 506 {
 507         use_return_type=true;
 508         return_type=rt;
 509         return_type_tinfo=rtt;
 510         return *this;
 511 }
 512
 513 function_options & function_options::do_not_evalf_params(void)
 514 {
 515         evalf_params_first=false;
 516         return *this;
 517 }
 518
 519 function_options & function_options::remember(unsigned size,
 520                                               unsigned assoc_size,
 521                                               unsigned strategy)
 522 {
 523         use_remember=true;
 524         remember_size=size;
 525         remember_assoc_size=assoc_size;
 526         remember_strategy=strategy;
 527         return *this;
 528 }
 529
 530 function_options & function_options::overloaded(unsigned o)
 531 {
 532         functions_with_same_name=o;
 533         return *this;
 534 }
 535
 536 function_options & function_options::set_symmetry(const symmetry & s)
 537 {
 538         symtree = s;
 539         return *this;
 540 }
 541
 542 void function_options::test_and_set_nparams(unsigned n)
 543 {
 544         if (nparams==0) {
 545                 nparams=n;
 546         } else if (nparams!=n) {
 547                 // we do not throw an exception here because this code is
 548                 // usually executed before main(), so the exception could not
 549                 // caught anyhow
 550                 std::cerr << "WARNING: number of parameters ("
 551                           << n << ") differs from number set before ("
 552                           << nparams << ")" << std::endl;
 553         }
 554 }
 555
 556 GINAC_IMPLEMENT_REGISTERED_CLASS(function, exprseq)
 557
 558 //////////
 559 // default ctor, dtor, copy ctor assignment operator and helpers
 560 //////////
 561
 562 // public
 563
 564 function::function() : serial(0)
 565 {
 566         debugmsg("function default ctor",LOGLEVEL_CONSTRUCT);
 567         tinfo_key = TINFO_function;
 568 }
 569
 570 // protected
 571
 572 void function::copy(const function & other)
 573 {
 574         exprseq::copy(other);
 575         serial=other.serial;
 576 }
 577
 578 void function::destroy(bool call_parent)
 579 {
 580         if (call_parent) exprseq::destroy(call_parent);
 581 }
 582
 583 //////////
 584 // other ctors
 585 //////////
 586
 587 // public
 588
 589 function::function(unsigned ser) : serial(ser)
 590 {
 591         debugmsg("function ctor from unsigned",LOGLEVEL_CONSTRUCT);
 592         tinfo_key = TINFO_function;
 593 }
 594
 595 // the following lines have been generated for max. ${maxargs} parameters
 596 $constructors_implementation
 597 // end of generated lines
 598
 599 function::function(unsigned ser, const exprseq & es) : exprseq(es), serial(ser)
 600 {
 601         debugmsg("function ctor from unsigned,exprseq",LOGLEVEL_CONSTRUCT);
 602         tinfo_key = TINFO_function;
 603 }
 604
 605 function::function(unsigned ser, const exvector & v, bool discardable)
 606   : exprseq(v,discardable), serial(ser)
 607 {
 608         debugmsg("function ctor from string,exvector,bool",LOGLEVEL_CONSTRUCT);
 609         tinfo_key = TINFO_function;
 610 }
 611
 612 function::function(unsigned ser, exvector * vp)
 613   : exprseq(vp), serial(ser)
 614 {
 615         debugmsg("function ctor from unsigned,exvector *",LOGLEVEL_CONSTRUCT);
 616         tinfo_key = TINFO_function;
 617 }
 618
 619 //////////
 620 // archiving
 621 //////////
 622
 623 /** Construct object from archive_node. */
 624 function::function(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
 625 {
 626         debugmsg("function ctor from archive_node", LOGLEVEL_CONSTRUCT);
 627
 628         // Find serial number by function name
 629         std::string s;
 630         if (n.find_string("name", s)) {
 631                 unsigned int ser = 0;
 632                 std::vector<function_options>::const_iterator i = registered_functions().begin(), iend = registered_functions().end();
 633                 while (i != iend) {
 634                         if (s == i->name) {
 635                                 serial = ser;
 636                                 return;
 637                         }
 638                         i++; ser++;
 639                 }
 640                 throw (std::runtime_error("unknown function '" + s + "' in archive"));
 641         } else
 642                 throw (std::runtime_error("unnamed function in archive"));
 643 }
 644
 645 /** Unarchive the object. */
 646 ex function::unarchive(const archive_node &n, const lst &sym_lst)
 647 {
 648         return (new function(n, sym_lst))->setflag(status_flags::dynallocated);
 649 }
 650
 651 /** Archive the object. */
 652 void function::archive(archive_node &n) const
 653 {
 654         inherited::archive(n);
 655         GINAC_ASSERT(serial < registered_functions().size());
 656         n.add_string("name", registered_functions()[serial].name);
 657 }
 658
 659 //////////
 660 // functions overriding virtual functions from bases classes
 661 //////////
 662
 663 // public
 664
 665 void function::print(const print_context & c, unsigned level) const
 666 {
 667         debugmsg("function print", LOGLEVEL_PRINT);
 668
 669         GINAC_ASSERT(serial<registered_functions().size());
 670
 671         if (is_of_type(c, print_tree)) {
 672
 673                 c.s << std::string(level, ' ') << class_name() << " "
 674                     << registered_functions()[serial].name
 675                     << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
 676                     << ", nops=" << nops()
 677                     << std::endl;
 678                 unsigned delta_indent = static_cast<const print_tree &>(c).delta_indent;
 679                 for (unsigned i=0; i<nops(); ++i)
 680                         seq[i].print(c, level + delta_indent);
 681                 c.s << std::string(level + delta_indent, ' ') << "=====" << std::endl;
 682
 683         } else if (is_of_type(c, print_csrc)) {
 684
 685                 // Print function name in lowercase
 686                 std::string lname = registered_functions()[serial].name;
 687                 for (unsigned i=0; i<lname.size(); i++)
 688                         lname[i] = tolower(lname[i]);
 689                 c.s << lname << "(";
 690
 691                 // Print arguments, separated by commas
 692                 exvector::const_iterator it = seq.begin(), itend = seq.end();
 693                 while (it != itend) {
 694                         it->print(c);
 695                         it++;
 696                         if (it != itend)
 697                                 c.s << ",";
 698                 }
 699                 c.s << ")";
 700
 701         } else if (is_of_type(c, print_latex)) {
 702                 c.s << registered_functions()[serial].TeX_name;
 703                 printseq(c, '(', ',', ')', exprseq::precedence(), function::precedence());
 704         } else {
 705                 c.s << registered_functions()[serial].name;
 706                 printseq(c, '(', ',', ')', exprseq::precedence(), function::precedence());
 707         }
 708 }
 709
 710 ex function::expand(unsigned options) const
 711 {
 712         return this->setflag(status_flags::expanded);
 713 }
 714
 715 int function::degree(const ex & s) const
 716 {
 717         return is_equal(*s.bp) ? 1 : 0;
 718 }
 719
 720 int function::ldegree(const ex & s) const
 721 {
 722         return is_equal(*s.bp) ? 1 : 0;
 723 }
 724
 725 ex function::coeff(const ex & s, int n) const
 726 {
 727         if (is_equal(*s.bp))
 728                 return n==1 ? _ex1() : _ex0();
 729         else
 730                 return n==0 ? ex(*this) : _ex0();
 731 }
 732
 733 ex function::eval(int level) const
 734 {
 735         GINAC_ASSERT(serial<registered_functions().size());
 736
 737         if (level>1) {
 738                 // first evaluate children, then we will end up here again
 739                 return function(serial,evalchildren(level));
 740         }
 741
 742         const function_options &opt = registered_functions()[serial];
 743
 744         // Canonicalize argument order according to the symmetry properties
 745         if (seq.size() > 1 && !(opt.symtree.is_zero())) {
 746                 exvector v = seq;
 747                 GINAC_ASSERT(is_ex_exactly_of_type(opt.symtree, symmetry));
 748                 int sig = canonicalize(v.begin(), ex_to_symmetry(opt.symtree));
 749                 if (sig != INT_MAX) {
 750                         // Something has changed while sorting arguments, more evaluations later
 751                         if (sig == 0)
 752                                 return _ex0();
 753                         return ex(sig) * thisexprseq(v);
 754                 }
 755         }
 756
 757         if (opt.eval_f==0) {
 758                 return this->hold();
 759         }
 760
 761         bool use_remember=opt.use_remember;
 762         ex eval_result;
 763         if (use_remember && lookup_remember_table(eval_result)) {
 764                 return eval_result;
 765         }
 766
 767         switch (opt.nparams) {
 768                 // the following lines have been generated for max. ${maxargs} parameters
 769 ${eval_switch_statement}
 770                 // end of generated lines
 771         default:
 772                 throw(std::logic_error("function::eval(): invalid nparams"));
 773         }
 774         if (use_remember) {
 775                 store_remember_table(eval_result);
 776         }
 777         return eval_result;
 778 }
 779
 780 ex function::evalf(int level) const
 781 {
 782         GINAC_ASSERT(serial<registered_functions().size());
 783
 784         exvector eseq=evalfchildren(level);
 785
 786         if (registered_functions()[serial].evalf_f==0) {
 787                 return function(serial,eseq).hold();
 788         }
 789         switch (registered_functions()[serial].nparams) {
 790                 // the following lines have been generated for max. ${maxargs} parameters
 791 ${evalf_switch_statement}
 792                 // end of generated lines
 793         }
 794         throw(std::logic_error("function::evalf(): invalid nparams"));
 795 }
 796
 797 unsigned function::calchash(void) const
 798 {
 799         unsigned v = golden_ratio_hash(golden_ratio_hash(tinfo()) ^ serial);
 800         for (unsigned i=0; i<nops(); i++) {
 801                 v = rotate_left_31(v);
 802                 v ^= this->op(i).gethash();
 803         }
 804         v &= 0x7FFFFFFFU;
 805         if (flags & status_flags::evaluated) {
 806                 setflag(status_flags::hash_calculated);
 807                 hashvalue = v;
 808         }
 809         return v;
 810 }
 811
 812 ex function::thisexprseq(const exvector & v) const
 813 {
 814         return function(serial,v);
 815 }
 816
 817 ex function::thisexprseq(exvector * vp) const
 818 {
 819         return function(serial,vp);
 820 }
 821
 822 /** Implementation of ex::series for functions.
 823  *  \@see ex::series */
 824 ex function::series(const relational & r, int order, unsigned options) const
 825 {
 826         GINAC_ASSERT(serial<registered_functions().size());
 827
 828         if (registered_functions()[serial].series_f==0) {
 829                 return basic::series(r, order);
 830         }
 831         ex res;
 832         switch (registered_functions()[serial].nparams) {
 833                 // the following lines have been generated for max. ${maxargs} parameters
 834 ${series_switch_statement}
 835                 // end of generated lines
 836         }
 837         throw(std::logic_error("function::series(): invalid nparams"));
 838 }
 839
 840 bool function::match(const ex & pattern, lst & repl_lst) const
 841 {
 842         // Serial number must match
 843         if (is_ex_of_type(pattern, function) && serial != ex_to_function(pattern).serial)
 844                 return false;
 845         return inherited::match(pattern, repl_lst);
 846 }
 847
 848 // protected
 849
 850
 851 /** Implementation of ex::diff() for functions. It applies the chain rule,
 852  *  except for the Order term function.
 853  *  \@see ex::diff */
 854 ex function::derivative(const symbol & s) const
 855 {
 856         ex result;
 857
 858         if (serial == function_index_Order) {
 859                 // Order Term function only differentiates the argument
 860                 return Order(seq[0].diff(s));
 861         } else if (serial == function_index_Derivative) {
 862                 // Inert derivative performs chain rule on the first argument only, and
 863                 // adds differentiation parameter to list (second argument)
 864                 GINAC_ASSERT(is_ex_exactly_of_type(seq[0], function));
 865                 GINAC_ASSERT(is_ex_exactly_of_type(seq[1], function));
 866                 ex fcn = seq[0];
 867                 ex arg_diff;
 868                 for (unsigned i=0; i!=fcn.nops(); i++) {
 869                         arg_diff = fcn.op(i).diff(s);
 870                         if (!arg_diff.is_zero()) {
 871                                 lst new_lst = ex_to_lst(seq[1]);
 872                                 new_lst.append(i);
 873                                 result += arg_diff * Derivative(fcn, new_lst);
 874                         }
 875                 }
 876         } else {
 877                 // Chain rule
 878                 ex arg_diff;
 879                 for (unsigned i=0; i!=seq.size(); i++) {
 880                         arg_diff = seq[i].diff(s);
 881                         // We apply the chain rule only when it makes sense.  This is not
 882                         // just for performance reasons but also to allow functions to
 883                         // throw when differentiated with respect to one of its arguments
 884                         // without running into trouble with our automatic full
 885                         // differentiation:
 886                         if (!arg_diff.is_zero())
 887                                 result += pderivative(i)*arg_diff;
 888                 }
 889         }
 890         return result;
 891 }
 892
 893 int function::compare_same_type(const basic & other) const
 894 {
 895         GINAC_ASSERT(is_of_type(other, function));
 896         const function & o=static_cast<function &>(const_cast<basic &>(other));
 897
 898         if (serial!=o.serial) {
 899                 return serial < o.serial ? -1 : 1;
 900         }
 901         return exprseq::compare_same_type(o);
 902 }
 903
 904 bool function::is_equal_same_type(const basic & other) const
 905 {
 906         GINAC_ASSERT(is_of_type(other, function));
 907         const function & o=static_cast<function &>(const_cast<basic &>(other));
 908
 909         if (serial!=o.serial) return false;
 910         return exprseq::is_equal_same_type(o);
 911 }
 912
 913 unsigned function::return_type(void) const
 914 {
 915         if (seq.size()==0) {
 916                 return return_types::commutative;
 917         }
 918         return (*seq.begin()).return_type();
 919 }
 920
 921 unsigned function::return_type_tinfo(void) const
 922 {
 923         if (seq.size()==0) {
 924                 return tinfo_key;
 925         }
 926         return (*seq.begin()).return_type_tinfo();
 927 }
 928
 929 //////////
 930 // new virtual functions which can be overridden by derived classes
 931 //////////
 932
 933 // none
 934
 935 //////////
 936 // non-virtual functions in this class
 937 //////////
 938
 939 // protected
 940
 941 ex function::pderivative(unsigned diff_param) const // partial differentiation
 942 {
 943         GINAC_ASSERT(serial<registered_functions().size());
 944
 945         if (registered_functions()[serial].derivative_f==0) {
 946                 return Derivative(*this, lst(ex(diff_param)));
 947         }
 948         switch (registered_functions()[serial].nparams) {
 949                 // the following lines have been generated for max. ${maxargs} parameters
 950 ${diff_switch_statement}
 951                 // end of generated lines
 952         }
 953         throw(std::logic_error("function::pderivative(): no diff function defined"));
 954 }
 955
 956 std::vector<function_options> & function::registered_functions(void)
 957 {
 958         static std::vector<function_options> * rf = new std::vector<function_options>;
 959         return *rf;
 960 }
 961
 962 bool function::lookup_remember_table(ex & result) const
 963 {
 964         return remember_table::remember_tables()[serial].lookup_entry(*this,result);
 965 }
 966
 967 void function::store_remember_table(ex const & result) const
 968 {
 969         remember_table::remember_tables()[serial].add_entry(*this,result);
 970 }
 971
 972 // public
 973
 974 unsigned function::register_new(function_options const & opt)
 975 {
 976         unsigned same_name=0;
 977         for (unsigned i=0; i<registered_functions().size(); ++i) {
 978                 if (registered_functions()[i].name==opt.name) {
 979                         same_name++;
 980                 }
 981         }
 982         if (same_name>=opt.functions_with_same_name) {
 983                 // we do not throw an exception here because this code is
 984                 // usually executed before main(), so the exception could not
 985                 // caught anyhow
 986                 std::cerr << "WARNING: function name " << opt.name
 987                                   << " already in use!" << std::endl;
 988         }
 989         registered_functions().push_back(opt);
 990         if (opt.use_remember) {
 991                 remember_table::remember_tables().
 992                         push_back(remember_table(opt.remember_size,
 993                                                                          opt.remember_assoc_size,
 994                                                                          opt.remember_strategy));
 995         } else {
 996                 remember_table::remember_tables().push_back(remember_table());
 997         }
 998         return registered_functions().size()-1;
 999 }
1000
1001 /** Find serial number of function by name and number of parameters.
1002  *  Throws exception if function was not found. */
1003 unsigned function::find_function(const std::string &name, unsigned nparams)
1004 {
1005         std::vector<function_options>::const_iterator i = function::registered_functions().begin(), end = function::registered_functions().end();
1006         unsigned serial = 0;
1007         while (i != end) {
1008                 if (i->get_name() == name && i->get_nparams() == nparams)
1009                         return serial;
1010                 i++;
1011                 serial++;
1012         }
1013         throw (std::runtime_error("no function '" + name + "' with " + ToString(nparams) + " parameters defined"));
1014 }
1015
1016 /** Return the print name of the function. */
1017 std::string function::get_name(void) const
1018 {
1019         GINAC_ASSERT(serial<registered_functions().size());
1020         return registered_functions()[serial].name;
1021 }
1022
1023 } // namespace GiNaC
1024
1025 END_OF_IMPLEMENTATION
1026
1027 print "Creating interface file function.h...";
1028 open OUT,">function.h" or die "cannot open function.h";
1029 print OUT $interface;
1030 close OUT;
1031 print "ok.\n";
1032
1033 print "Creating implementation file function.cpp...";
1034 open OUT,">function.cpp" or die "cannot open function.cpp";
1035 print OUT $implementation;
1036 close OUT;
1037 print "ok.\n";
1038
1039 print "done.\n";