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