ginac/function.pl

   1 $maxargs=13;
   2
   3 sub generate_seq {
   4         my ($seq_template,$n)=@_;
   5         my ($res,$N);
   6
   7         $res='';
   8         for ($N=1; $N<=$n; $N++) {
   9                 $res .= eval('"' . $seq_template . '"');
  10                 if ($N!=$n) {
  11                         $res .= ', ';
  12                 }
  13         }
  14         return $res;
  15 }
  16
  17 sub generate_from_to {
  18         my ($template,$seq_template1,$seq_template2,$seq_template3,$from,$to)=@_;
  19         my ($res,$N,$SEQ);
  20
  21         $res='';
  22         for ($N=$from; $N<=$to; $N++) {
  23                 $SEQ1=generate_seq($seq_template1,$N);
  24                 $SEQ2=generate_seq($seq_template2,$N);
  25                 $SEQ3=generate_seq($seq_template3,$N);
  26                 $res .= eval('"' . $template . '"');
  27                 $SEQ1=''; # to avoid main::SEQ1 used only once warning
  28                 $SEQ2=''; # same as above
  29                 $SEQ3=''; # same as above
  30         }
  31         return $res;
  32 }
  33
  34 sub generate {
  35         my ($template,$seq_template1,$seq_template2,$seq_template3)=@_;
  36         return generate_from_to($template,$seq_template1,$seq_template2,$seq_template3,1,$maxargs);
  37 }
  38
  39 $declare_function_macro = generate(
  40         <<'END_OF_DECLARE_FUNCTION_MACRO','typename T${N}','const T${N} & p${N}','GiNaC::ex(p${N})');
  41 #define DECLARE_FUNCTION_${N}P(NAME) \\
  42 extern const unsigned function_index_##NAME; \\
  43 template<${SEQ1}> \\
  44 inline const GiNaC::function NAME(${SEQ2}) { \\
  45         return GiNaC::function(function_index_##NAME, ${SEQ3}); \\
  46 }
  47
  48 END_OF_DECLARE_FUNCTION_MACRO
  49
  50 $typedef_eval_funcp=generate(
  51 'typedef ex (* eval_funcp_${N})(${SEQ1});'."\n",
  52 'const ex &','','');
  53
  54 $typedef_evalf_funcp=generate(
  55 'typedef ex (* evalf_funcp_${N})(${SEQ1});'."\n",
  56 'const ex &','','');
  57
  58 $typedef_derivative_funcp=generate(
  59 'typedef ex (* derivative_funcp_${N})(${SEQ1}, unsigned);'."\n",
  60 'const ex &','','');
  61
  62 $typedef_series_funcp=generate(
  63 'typedef ex (* series_funcp_${N})(${SEQ1}, const relational &, int, unsigned);'."\n",
  64 'const ex &','','');
  65
  66 $eval_func_interface=generate('    function_options & eval_func(eval_funcp_${N} e);'."\n",'','','');
  67
  68 $evalf_func_interface=generate('    function_options & evalf_func(evalf_funcp_${N} ef);'."\n",'','','');
  69
  70 $derivative_func_interface=generate('    function_options & derivative_func(derivative_funcp_${N} d);'."\n",'','','');
  71
  72 $series_func_interface=generate('    function_options & series_func(series_funcp_${N} s);'."\n",'','','');
  73
  74 $constructors_interface=generate(
  75 '    function(unsigned ser, ${SEQ1});'."\n",
  76 'const ex & param${N}','','');
  77
  78 $constructors_implementation=generate(
  79         <<'END_OF_CONSTRUCTORS_IMPLEMENTATION','const ex & param${N}','param${N}','');
  80 function::function(unsigned ser, ${SEQ1})
  81         : exprseq(${SEQ2}), serial(ser)
  82 {
  83         debugmsg(\"function ctor from unsigned,${N}*ex\",LOGLEVEL_CONSTRUCT);
  84         tinfo_key = TINFO_function;
  85 }
  86 END_OF_CONSTRUCTORS_IMPLEMENTATION
  87
  88 $eval_switch_statement=generate(
  89         <<'END_OF_EVAL_SWITCH_STATEMENT','seq[${N}-1]','','');
  90         case ${N}:
  91                 eval_result = ((eval_funcp_${N})(registered_functions()[serial].eval_f))(${SEQ1});
  92                 break;
  93 END_OF_EVAL_SWITCH_STATEMENT
  94
  95 $evalf_switch_statement=generate(
  96         <<'END_OF_EVALF_SWITCH_STATEMENT','eseq[${N}-1]','','');
  97         case ${N}:
  98                 return ((evalf_funcp_${N})(registered_functions()[serial].evalf_f))(${SEQ1});
  99 END_OF_EVALF_SWITCH_STATEMENT
 100
 101 $diff_switch_statement=generate(
 102         <<'END_OF_DIFF_SWITCH_STATEMENT','seq[${N}-1]','','');
 103         case ${N}:
 104                 return ((derivative_funcp_${N})(registered_functions()[serial].derivative_f))(${SEQ1},diff_param);
 105 END_OF_DIFF_SWITCH_STATEMENT
 106
 107 $series_switch_statement=generate(
 108         <<'END_OF_SERIES_SWITCH_STATEMENT','seq[${N}-1]','','');
 109         case ${N}:
 110                 try {
 111                         res = ((series_funcp_${N})(registered_functions()[serial].series_f))(${SEQ1},r,order,options);
 112                 } catch (do_taylor) {
 113                         res = basic::series(r, order, options);
 114                 }
 115                 return res;
 116 END_OF_SERIES_SWITCH_STATEMENT
 117
 118 $eval_func_implementation=generate(
 119         <<'END_OF_EVAL_FUNC_IMPLEMENTATION','','','');
 120 function_options & function_options::eval_func(eval_funcp_${N} e)
 121 {
 122         test_and_set_nparams(${N});
 123         eval_f = eval_funcp(e);
 124         return *this;
 125 }
 126 END_OF_EVAL_FUNC_IMPLEMENTATION
 127
 128 $evalf_func_implementation=generate(
 129         <<'END_OF_EVALF_FUNC_IMPLEMENTATION','','','');
 130 function_options & function_options::evalf_func(evalf_funcp_${N} ef)
 131 {
 132         test_and_set_nparams(${N});
 133         evalf_f = evalf_funcp(ef);
 134         return *this;
 135 }
 136 END_OF_EVALF_FUNC_IMPLEMENTATION
 137
 138 $derivative_func_implementation=generate(
 139         <<'END_OF_DERIVATIVE_FUNC_IMPLEMENTATION','','','');
 140 function_options & function_options::derivative_func(derivative_funcp_${N} d)
 141 {
 142         test_and_set_nparams(${N});
 143         derivative_f = derivative_funcp(d);
 144         return *this;
 145 }
 146 END_OF_DERIVATIVE_FUNC_IMPLEMENTATION
 147
 148 $series_func_implementation=generate(
 149         <<'END_OF_SERIES_FUNC_IMPLEMENTATION','','','');
 150 function_options & function_options::series_func(series_funcp_${N} s)
 151 {
 152         test_and_set_nparams(${N});
 153         series_f = series_funcp(s);
 154         return *this;
 155 }
 156 END_OF_SERIES_FUNC_IMPLEMENTATION
 157
 158 $interface=<<END_OF_INTERFACE;
 159 /** \@file function.h
 160  *
 161  *  Interface to class of symbolic functions. */
 162
 163 /*
 164  *  This file was generated automatically by function.pl.
 165  *  Please do not modify it directly, edit the perl script instead!
 166  *  function.pl options: \$maxargs=${maxargs}
 167  *
 168  *  GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
 169  *
 170  *  This program is free software; you can redistribute it and/or modify
 171  *  it under the terms of the GNU General Public License as published by
 172  *  the Free Software Foundation; either version 2 of the License, or
 173  *  (at your option) any later version.
 174  *
 175  *  This program is distributed in the hope that it will be useful,
 176  *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 177  *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 178  *  GNU General Public License for more details.
 179  *
 180  *  You should have received a copy of the GNU General Public License
 181  *  along with this program; if not, write to the Free Software
 182  *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 183  */
 184
 185 #ifndef __GINAC_FUNCTION_H__
 186 #define __GINAC_FUNCTION_H__
 187
 188 #include <string>
 189 #include <vector>
 190
 191 // CINT needs <algorithm> to work properly with <vector>
 192 #include <algorithm>
 193
 194 #include "exprseq.h"
 195
 196 // the following lines have been generated for max. ${maxargs} parameters
 197 $declare_function_macro
 198 // end of generated lines
 199
 200 #define REGISTER_FUNCTION(NAME,OPT) \\
 201 const unsigned function_index_##NAME= \\
 202         GiNaC::function::register_new(GiNaC::function_options(#NAME).OPT);
 203
 204 #define BEGIN_TYPECHECK \\
 205 bool automatic_typecheck=true;
 206
 207 #define TYPECHECK(VAR,TYPE) \\
 208 if (!is_exactly_a<TYPE>(VAR)) { \\
 209         automatic_typecheck=false; \\
 210 } else
 211
 212 #define TYPECHECK_INTEGER(VAR) \\
 213 if (!(VAR).info(GiNaC::info_flags::integer)) { \\
 214         automatic_typecheck=false; \\
 215 } else
 216
 217 #define END_TYPECHECK(RV) \\
 218 {} \\
 219 if (!automatic_typecheck) { \\
 220         return RV.hold(); \\
 221 }
 222
 223 namespace GiNaC {
 224
 225 class function;
 226 class symmetry;
 227
 228 typedef ex (* eval_funcp)();
 229 typedef ex (* evalf_funcp)();
 230 typedef ex (* derivative_funcp)();
 231 typedef ex (* series_funcp)();
 232
 233 // the following lines have been generated for max. ${maxargs} parameters
 234 $typedef_eval_funcp
 235 $typedef_evalf_funcp
 236 $typedef_derivative_funcp
 237 $typedef_series_funcp
 238 // end of generated lines
 239
 240 class function_options
 241 {
 242         friend class function;
 243         friend class fderivative;
 244 public:
 245         function_options();
 246         function_options(std::string const & n, std::string const & tn=std::string());
 247         ~function_options();
 248         void initialize(void);
 249         function_options & set_name(std::string const & n, std::string const & tn=std::string());
 250         function_options & latex_name(std::string const & tn);
 251 // the following lines have been generated for max. ${maxargs} parameters
 252 $eval_func_interface
 253 $evalf_func_interface
 254 $derivative_func_interface
 255 $series_func_interface
 256 // end of generated lines
 257         function_options & set_return_type(unsigned rt, unsigned rtt=0);
 258         function_options & do_not_evalf_params(void);
 259         function_options & remember(unsigned size, unsigned assoc_size=0,
 260                                     unsigned strategy=remember_strategies::delete_never);
 261         function_options & overloaded(unsigned o);
 262         function_options & set_symmetry(const symmetry & s);
 263         void test_and_set_nparams(unsigned n);
 264         std::string get_name(void) const { return name; }
 265         unsigned get_nparams(void) const { return nparams; }
 266         bool has_derivative(void) const { return derivative_f != NULL; }
 267
 268 protected:
 269         std::string name;
 270         std::string TeX_name;
 271
 272         unsigned nparams;
 273
 274         eval_funcp eval_f;
 275         evalf_funcp evalf_f;
 276         derivative_funcp derivative_f;
 277         series_funcp series_f;
 278
 279         bool evalf_params_first;
 280
 281         bool use_return_type;
 282         unsigned return_type;
 283         unsigned return_type_tinfo;
 284
 285         bool use_remember;
 286         unsigned remember_size;
 287         unsigned remember_assoc_size;
 288         unsigned remember_strategy;
 289
 290         unsigned functions_with_same_name;
 291
 292         ex symtree;
 293 };
 294
 295 /** The class function is used to implement builtin functions like sin, cos...
 296         and user defined functions */
 297 class function : public exprseq
 298 {
 299         GINAC_DECLARE_REGISTERED_CLASS(function, exprseq)
 300
 301         // CINT has a linking problem
 302 #ifndef __MAKECINT__
 303         friend void ginsh_get_ginac_functions(void);
 304 #endif // def __MAKECINT__
 305
 306         friend class remember_table_entry;
 307         // friend class remember_table_list;
 308         // friend class remember_table;
 309
 310 // member functions
 311
 312         // other ctors
 313 public:
 314         function(unsigned ser);
 315         // the following lines have been generated for max. ${maxargs} parameters
 316 $constructors_interface
 317         // end of generated lines
 318         function(unsigned ser, const exprseq & es);
 319         function(unsigned ser, const exvector & v, bool discardable = false);
 320         function(unsigned ser, exvector * vp); // vp will be deleted
 321
 322         // functions overriding virtual functions from base classes
 323 public:
 324         void print(const print_context & c, unsigned level = 0) const;
 325         unsigned precedence(void) const {return 70;}
 326         int degree(const ex & s) const;
 327         int ldegree(const ex & s) const;
 328         ex coeff(const ex & s, int n = 1) const;
 329         ex expand(unsigned options=0) const;
 330         ex eval(int level=0) const;
 331         ex evalf(int level=0) const;
 332         unsigned calchash(void) const;
 333         ex series(const relational & r, int order, unsigned options = 0) const;
 334         ex thisexprseq(const exvector & v) const;
 335         ex thisexprseq(exvector * vp) const;
 336 protected:
 337         ex derivative(const symbol & s) const;
 338         bool is_equal_same_type(const basic & other) const;
 339         bool match_same_type(const basic & other) const;
 340         unsigned return_type(void) const;
 341         unsigned return_type_tinfo(void) const;
 342
 343         // new virtual functions which can be overridden by derived classes
 344         // none
 345
 346         // non-virtual functions in this class
 347 protected:
 348         ex pderivative(unsigned diff_param) const; // partial differentiation
 349         static std::vector<function_options> & registered_functions(void);
 350         bool lookup_remember_table(ex & result) const;
 351         void store_remember_table(ex const & result) const;
 352 public:
 353         static unsigned register_new(function_options const & opt);
 354         static unsigned find_function(const std::string &name, unsigned nparams);
 355         unsigned get_serial(void) const {return serial;}
 356         std::string get_name(void) const;
 357
 358 // member variables
 359
 360 protected:
 361         unsigned serial;
 362 };
 363
 364 // utility functions/macros
 365 /** Return the object of type function handled by an ex.
 366  *  This is unsafe: you need to check the type first. */
 367 inline const function &ex_to_function(const ex &e)
 368 {
 369         return static_cast<const function &>(*e.bp);
 370 }
 371
 372 /** Specialization of is_exactly_a<function>(obj) for objects of type function. */
 373 template<> inline bool is_exactly_a<function>(const basic & obj)
 374 {
 375         return obj.tinfo()==TINFO_function;
 376 }
 377
 378 #define is_ex_the_function(OBJ, FUNCNAME) \\
 379         (is_ex_exactly_of_type(OBJ, function) && static_cast<GiNaC::function *>(OBJ.bp)->get_serial() == function_index_##FUNCNAME)
 380
 381 } // namespace GiNaC
 382
 383 #endif // ndef __GINAC_FUNCTION_H__
 384
 385 END_OF_INTERFACE
 386
 387 $implementation=<<END_OF_IMPLEMENTATION;
 388 /** \@file function.cpp
 389  *
 390  *  Implementation of class of symbolic functions. */
 391
 392 /*
 393  *  This file was generated automatically by function.pl.
 394  *  Please do not modify it directly, edit the perl script instead!
 395  *  function.pl options: \$maxargs=${maxargs}
 396  *
 397  *  GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
 398  *
 399  *  This program is free software; you can redistribute it and/or modify
 400  *  it under the terms of the GNU General Public License as published by
 401  *  the Free Software Foundation; either version 2 of the License, or
 402  *  (at your option) any later version.
 403  *
 404  *  This program is distributed in the hope that it will be useful,
 405  *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 406  *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 407  *  GNU General Public License for more details.
 408  *
 409  *  You should have received a copy of the GNU General Public License
 410  *  along with this program; if not, write to the Free Software
 411  *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 412  */
 413
 414 #include <string>
 415 #include <stdexcept>
 416 #include <list>
 417
 418 #include "function.h"
 419 #include "fderivative.h"
 420 #include "ex.h"
 421 #include "lst.h"
 422 #include "symmetry.h"
 423 #include "print.h"
 424 #include "archive.h"
 425 #include "inifcns.h"
 426 #include "tostring.h"
 427 #include "utils.h"
 428 #include "debugmsg.h"
 429 #include "remember.h"
 430
 431 namespace GiNaC {
 432
 433 //////////
 434 // helper class function_options
 435 //////////
 436
 437 function_options::function_options()
 438 {
 439         initialize();
 440 }
 441
 442 function_options::function_options(std::string const & n, std::string const & tn)
 443 {
 444         initialize();
 445         set_name(n,tn);
 446 }
 447
 448 function_options::~function_options()
 449 {
 450         // nothing to clean up at the moment
 451 }
 452
 453 void function_options::initialize(void)
 454 {
 455         set_name("unnamed_function","\\\\mbox{unnamed}");
 456         nparams = 0;
 457         eval_f = evalf_f = derivative_f = series_f = 0;
 458         evalf_params_first = true;
 459         use_return_type = false;
 460         use_remember = false;
 461         functions_with_same_name = 1;
 462         symtree = 0;
 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         return *this;
 474 }
 475
 476 function_options & function_options::latex_name(std::string const & tn)
 477 {
 478         TeX_name=tn;
 479         return *this;
 480 }
 481
 482 // the following lines have been generated for max. ${maxargs} parameters
 483 $eval_func_implementation
 484 $evalf_func_implementation
 485 $derivative_func_implementation
 486 $series_func_implementation
 487 // end of generated lines
 488
 489 function_options & function_options::set_return_type(unsigned rt, unsigned rtt)
 490 {
 491         use_return_type = true;
 492         return_type = rt;
 493         return_type_tinfo = rtt;
 494         return *this;
 495 }
 496
 497 function_options & function_options::do_not_evalf_params(void)
 498 {
 499         evalf_params_first = false;
 500         return *this;
 501 }
 502
 503 function_options & function_options::remember(unsigned size,
 504                                               unsigned assoc_size,
 505                                               unsigned strategy)
 506 {
 507         use_remember = true;
 508         remember_size = size;
 509         remember_assoc_size = assoc_size;
 510         remember_strategy = strategy;
 511         return *this;
 512 }
 513
 514 function_options & function_options::overloaded(unsigned o)
 515 {
 516         functions_with_same_name = o;
 517         return *this;
 518 }
 519
 520 function_options & function_options::set_symmetry(const symmetry & s)
 521 {
 522         symtree = s;
 523         return *this;
 524 }
 525
 526 void function_options::test_and_set_nparams(unsigned n)
 527 {
 528         if (nparams==0) {
 529                 nparams = n;
 530         } else if (nparams!=n) {
 531                 // we do not throw an exception here because this code is
 532                 // usually executed before main(), so the exception could not
 533                 // caught anyhow
 534                 std::cerr << "WARNING: number of parameters ("
 535                           << n << ") differs from number set before ("
 536                           << nparams << ")" << std::endl;
 537         }
 538 }
 539
 540 GINAC_IMPLEMENT_REGISTERED_CLASS(function, exprseq)
 541
 542 //////////
 543 // default ctor, dtor, copy ctor assignment operator and helpers
 544 //////////
 545
 546 // public
 547
 548 function::function() : serial(0)
 549 {
 550         debugmsg("function default ctor",LOGLEVEL_CONSTRUCT);
 551         tinfo_key = TINFO_function;
 552 }
 553
 554 // protected
 555
 556 void function::copy(const function & other)
 557 {
 558         inherited::copy(other);
 559         serial = other.serial;
 560 }
 561
 562 void function::destroy(bool call_parent)
 563 {
 564         if (call_parent)
 565                 inherited::destroy(call_parent);
 566 }
 567
 568 //////////
 569 // other ctors
 570 //////////
 571
 572 // public
 573
 574 function::function(unsigned ser) : serial(ser)
 575 {
 576         debugmsg("function ctor from unsigned",LOGLEVEL_CONSTRUCT);
 577         tinfo_key = TINFO_function;
 578 }
 579
 580 // the following lines have been generated for max. ${maxargs} parameters
 581 $constructors_implementation
 582 // end of generated lines
 583
 584 function::function(unsigned ser, const exprseq & es) : exprseq(es), serial(ser)
 585 {
 586         debugmsg("function ctor from unsigned,exprseq",LOGLEVEL_CONSTRUCT);
 587         tinfo_key = TINFO_function;
 588 }
 589
 590 function::function(unsigned ser, const exvector & v, bool discardable)
 591   : exprseq(v,discardable), serial(ser)
 592 {
 593         debugmsg("function ctor from string,exvector,bool",LOGLEVEL_CONSTRUCT);
 594         tinfo_key = TINFO_function;
 595 }
 596
 597 function::function(unsigned ser, exvector * vp)
 598   : exprseq(vp), serial(ser)
 599 {
 600         debugmsg("function ctor from unsigned,exvector *",LOGLEVEL_CONSTRUCT);
 601         tinfo_key = TINFO_function;
 602 }
 603
 604 //////////
 605 // archiving
 606 //////////
 607
 608 /** Construct object from archive_node. */
 609 function::function(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
 610 {
 611         debugmsg("function ctor from archive_node", LOGLEVEL_CONSTRUCT);
 612
 613         // Find serial number by function name
 614         std::string s;
 615         if (n.find_string("name", s)) {
 616                 unsigned int ser = 0;
 617                 std::vector<function_options>::const_iterator i = registered_functions().begin(), iend = registered_functions().end();
 618                 while (i != iend) {
 619                         if (s == i->name) {
 620                                 serial = ser;
 621                                 return;
 622                         }
 623                         ++i; ++ser;
 624                 }
 625                 throw (std::runtime_error("unknown function '" + s + "' in archive"));
 626         } else
 627                 throw (std::runtime_error("unnamed function in archive"));
 628 }
 629
 630 /** Unarchive the object. */
 631 ex function::unarchive(const archive_node &n, const lst &sym_lst)
 632 {
 633         return (new function(n, sym_lst))->setflag(status_flags::dynallocated);
 634 }
 635
 636 /** Archive the object. */
 637 void function::archive(archive_node &n) const
 638 {
 639         inherited::archive(n);
 640         GINAC_ASSERT(serial < registered_functions().size());
 641         n.add_string("name", registered_functions()[serial].name);
 642 }
 643
 644 //////////
 645 // functions overriding virtual functions from base classes
 646 //////////
 647
 648 // public
 649
 650 void function::print(const print_context & c, unsigned level) const
 651 {
 652         debugmsg("function print", LOGLEVEL_PRINT);
 653
 654         GINAC_ASSERT(serial<registered_functions().size());
 655
 656         if (is_of_type(c, print_tree)) {
 657
 658                 c.s << std::string(level, ' ') << class_name() << " "
 659                     << registered_functions()[serial].name
 660                     << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
 661                     << ", nops=" << nops()
 662                     << std::endl;
 663                 unsigned delta_indent = static_cast<const print_tree &>(c).delta_indent;
 664                 for (unsigned i=0; i<seq.size(); ++i)
 665                         seq[i].print(c, level + delta_indent);
 666                 c.s << std::string(level + delta_indent, ' ') << "=====" << std::endl;
 667
 668         } else if (is_of_type(c, print_csrc)) {
 669
 670                 // Print function name in lowercase
 671                 std::string lname = registered_functions()[serial].name;
 672                 unsigned num = lname.size();
 673                 for (unsigned i=0; i<num; i++)
 674                         lname[i] = tolower(lname[i]);
 675                 c.s << lname << "(";
 676
 677                 // Print arguments, separated by commas
 678                 exvector::const_iterator it = seq.begin(), itend = seq.end();
 679                 while (it != itend) {
 680                         it->print(c);
 681                         ++it;
 682                         if (it != itend)
 683                                 c.s << ",";
 684                 }
 685                 c.s << ")";
 686
 687         } else if (is_of_type(c, print_latex)) {
 688                 c.s << registered_functions()[serial].TeX_name;
 689                 printseq(c, '(', ',', ')', exprseq::precedence(), function::precedence());
 690         } else {
 691                 c.s << registered_functions()[serial].name;
 692                 printseq(c, '(', ',', ')', exprseq::precedence(), function::precedence());
 693         }
 694 }
 695
 696 ex function::expand(unsigned options) const
 697 {
 698         // Only expand arguments when asked to do so
 699         if (options & expand_options::expand_function_args)
 700                 return inherited::expand(options);
 701         else
 702                 return (options == 0) ? setflag(status_flags::expanded) : *this;
 703 }
 704
 705 int function::degree(const ex & s) const
 706 {
 707         return is_equal(*s.bp) ? 1 : 0;
 708 }
 709
 710 int function::ldegree(const ex & s) const
 711 {
 712         return is_equal(*s.bp) ? 1 : 0;
 713 }
 714
 715 ex function::coeff(const ex & s, int n) const
 716 {
 717         if (is_equal(*s.bp))
 718                 return n==1 ? _ex1() : _ex0();
 719         else
 720                 return n==0 ? ex(*this) : _ex0();
 721 }
 722
 723 ex function::eval(int level) const
 724 {
 725         GINAC_ASSERT(serial<registered_functions().size());
 726
 727         if (level>1) {
 728                 // first evaluate children, then we will end up here again
 729                 return function(serial,evalchildren(level));
 730         }
 731
 732         const function_options &opt = registered_functions()[serial];
 733
 734         // Canonicalize argument order according to the symmetry properties
 735         if (seq.size() > 1 && !(opt.symtree.is_zero())) {
 736                 exvector v = seq;
 737                 GINAC_ASSERT(is_a<symmetry>(opt.symtree));
 738                 int sig = canonicalize(v.begin(), ex_to<symmetry>(opt.symtree));
 739                 if (sig != INT_MAX) {
 740                         // Something has changed while sorting arguments, more evaluations later
 741                         if (sig == 0)
 742                                 return _ex0();
 743                         return ex(sig) * thisexprseq(v);
 744                 }
 745         }
 746
 747         if (opt.eval_f==0) {
 748                 return this->hold();
 749         }
 750
 751         bool use_remember = opt.use_remember;
 752         ex eval_result;
 753         if (use_remember && lookup_remember_table(eval_result)) {
 754                 return eval_result;
 755         }
 756
 757         switch (opt.nparams) {
 758                 // the following lines have been generated for max. ${maxargs} parameters
 759 ${eval_switch_statement}
 760                 // end of generated lines
 761         default:
 762                 throw(std::logic_error("function::eval(): invalid nparams"));
 763         }
 764         if (use_remember) {
 765                 store_remember_table(eval_result);
 766         }
 767         return eval_result;
 768 }
 769
 770 ex function::evalf(int level) const
 771 {
 772         GINAC_ASSERT(serial<registered_functions().size());
 773
 774         // Evaluate children first
 775         exvector eseq;
 776         if (level == 1)
 777                 eseq = seq;
 778         else if (level == -max_recursion_level)
 779                 throw(std::runtime_error("max recursion level reached"));
 780         else
 781                 eseq.reserve(seq.size());
 782         --level;
 783         exvector::const_iterator it = seq.begin(), itend = seq.end();
 784         while (it != itend) {
 785                 eseq.push_back(it->evalf(level));
 786                 ++it;
 787         }
 788
 789         if (registered_functions()[serial].evalf_f==0) {
 790                 return function(serial,eseq).hold();
 791         }
 792         switch (registered_functions()[serial].nparams) {
 793                 // the following lines have been generated for max. ${maxargs} parameters
 794 ${evalf_switch_statement}
 795                 // end of generated lines
 796         }
 797         throw(std::logic_error("function::evalf(): invalid nparams"));
 798 }
 799
 800 unsigned function::calchash(void) const
 801 {
 802         unsigned v = golden_ratio_hash(golden_ratio_hash(tinfo()) ^ serial);
 803         for (unsigned i=0; i<nops(); i++) {
 804                 v = rotate_left_31(v);
 805                 v ^= this->op(i).gethash();
 806         }
 807         v &= 0x7FFFFFFFU;
 808         if (flags & status_flags::evaluated) {
 809                 setflag(status_flags::hash_calculated);
 810                 hashvalue = v;
 811         }
 812         return v;
 813 }
 814
 815 ex function::thisexprseq(const exvector & v) const
 816 {
 817         return function(serial,v);
 818 }
 819
 820 ex function::thisexprseq(exvector * vp) const
 821 {
 822         return function(serial,vp);
 823 }
 824
 825 /** Implementation of ex::series for functions.
 826  *  \@see ex::series */
 827 ex function::series(const relational & r, int order, unsigned options) const
 828 {
 829         GINAC_ASSERT(serial<registered_functions().size());
 830
 831         if (registered_functions()[serial].series_f==0) {
 832                 return basic::series(r, order);
 833         }
 834         ex res;
 835         switch (registered_functions()[serial].nparams) {
 836                 // the following lines have been generated for max. ${maxargs} parameters
 837 ${series_switch_statement}
 838                 // end of generated lines
 839         }
 840         throw(std::logic_error("function::series(): invalid nparams"));
 841 }
 842
 843 // protected
 844
 845 /** Implementation of ex::diff() for functions. It applies the chain rule,
 846  *  except for the Order term function.
 847  *  \@see ex::diff */
 848 ex function::derivative(const symbol & s) const
 849 {
 850         ex result;
 851
 852         if (serial == function_index_Order) {
 853                 // Order Term function only differentiates the argument
 854                 return Order(seq[0].diff(s));
 855         } else {
 856                 // Chain rule
 857                 ex arg_diff;
 858                 unsigned num = seq.size();
 859                 for (unsigned i=0; i<num; i++) {
 860                         arg_diff = seq[i].diff(s);
 861                         // We apply the chain rule only when it makes sense.  This is not
 862                         // just for performance reasons but also to allow functions to
 863                         // throw when differentiated with respect to one of its arguments
 864                         // without running into trouble with our automatic full
 865                         // differentiation:
 866                         if (!arg_diff.is_zero())
 867                                 result += pderivative(i)*arg_diff;
 868                 }
 869         }
 870         return result;
 871 }
 872
 873 int function::compare_same_type(const basic & other) const
 874 {
 875         GINAC_ASSERT(is_of_type(other, function));
 876         const function & o = static_cast<const function &>(other);
 877
 878         if (serial != o.serial)
 879                 return serial < o.serial ? -1 : 1;
 880         else
 881                 return exprseq::compare_same_type(o);
 882 }
 883
 884 bool function::is_equal_same_type(const basic & other) const
 885 {
 886         GINAC_ASSERT(is_of_type(other, function));
 887         const function & o = static_cast<const function &>(other);
 888
 889         if (serial != o.serial)
 890                 return false;
 891         else
 892                 return exprseq::is_equal_same_type(o);
 893 }
 894
 895 bool function::match_same_type(const basic & other) const
 896 {
 897         GINAC_ASSERT(is_of_type(other, function));
 898         const function & o = static_cast<const function &>(other);
 899
 900         return serial == o.serial;
 901 }
 902
 903 unsigned function::return_type(void) const
 904 {
 905         if (seq.empty())
 906                 return return_types::commutative;
 907         else
 908                 return seq.begin()->return_type();
 909 }
 910
 911 unsigned function::return_type_tinfo(void) const
 912 {
 913         if (seq.empty())
 914                 return tinfo_key;
 915         else
 916                 return seq.begin()->return_type_tinfo();
 917 }
 918
 919 //////////
 920 // new virtual functions which can be overridden by derived classes
 921 //////////
 922
 923 // none
 924
 925 //////////
 926 // non-virtual functions in this class
 927 //////////
 928
 929 // protected
 930
 931 ex function::pderivative(unsigned diff_param) const // partial differentiation
 932 {
 933         GINAC_ASSERT(serial<registered_functions().size());
 934
 935         // No derivative defined? Then return abstract derivative object
 936         if (registered_functions()[serial].derivative_f == NULL)
 937                 return fderivative(serial, diff_param, seq);
 938
 939         switch (registered_functions()[serial].nparams) {
 940                 // the following lines have been generated for max. ${maxargs} parameters
 941 ${diff_switch_statement}
 942                 // end of generated lines
 943         }
 944         throw(std::logic_error("function::pderivative(): no diff function defined"));
 945 }
 946
 947 std::vector<function_options> & function::registered_functions(void)
 948 {
 949         static std::vector<function_options> * rf = new std::vector<function_options>;
 950         return *rf;
 951 }
 952
 953 bool function::lookup_remember_table(ex & result) const
 954 {
 955         return remember_table::remember_tables()[serial].lookup_entry(*this,result);
 956 }
 957
 958 void function::store_remember_table(ex const & result) const
 959 {
 960         remember_table::remember_tables()[serial].add_entry(*this,result);
 961 }
 962
 963 // public
 964
 965 unsigned function::register_new(function_options const & opt)
 966 {
 967         unsigned same_name = 0;
 968         for (unsigned i=0; i<registered_functions().size(); ++i) {
 969                 if (registered_functions()[i].name==opt.name) {
 970                         ++same_name;
 971                 }
 972         }
 973         if (same_name>=opt.functions_with_same_name) {
 974                 // we do not throw an exception here because this code is
 975                 // usually executed before main(), so the exception could not
 976                 // caught anyhow
 977                 std::cerr << "WARNING: function name " << opt.name
 978                           << " already in use!" << std::endl;
 979         }
 980         registered_functions().push_back(opt);
 981         if (opt.use_remember) {
 982                 remember_table::remember_tables().
 983                         push_back(remember_table(opt.remember_size,
 984                                                  opt.remember_assoc_size,
 985                                                  opt.remember_strategy));
 986         } else {
 987                 remember_table::remember_tables().push_back(remember_table());
 988         }
 989         return registered_functions().size()-1;
 990 }
 991
 992 /** Find serial number of function by name and number of parameters.
 993  *  Throws exception if function was not found. */
 994 unsigned function::find_function(const std::string &name, unsigned nparams)
 995 {
 996         std::vector<function_options>::const_iterator i = function::registered_functions().begin(), end = function::registered_functions().end();
 997         unsigned serial = 0;
 998         while (i != end) {
 999                 if (i->get_name() == name && i->get_nparams() == nparams)
1000                         return serial;
1001                 ++i;
1002                 ++serial;
1003         }
1004         throw (std::runtime_error("no function '" + name + "' with " + ToString(nparams) + " parameters defined"));
1005 }
1006
1007 /** Return the print name of the function. */
1008 std::string function::get_name(void) const
1009 {
1010         GINAC_ASSERT(serial<registered_functions().size());
1011         return registered_functions()[serial].name;
1012 }
1013
1014 } // namespace GiNaC
1015
1016 END_OF_IMPLEMENTATION
1017
1018 print "Creating interface file function.h...";
1019 open OUT,">function.h" or die "cannot open function.h";
1020 print OUT $interface;
1021 close OUT;
1022 print "ok.\n";
1023
1024 print "Creating implementation file function.cpp...";
1025 open OUT,">function.cpp" or die "cannot open function.cpp";
1026 print OUT $implementation;
1027 close OUT;
1028 print "ok.\n";
1029
1030 print "done.\n";