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 // The TYPECHECK-macros were used inside the _evalf() functions.  They are
 205 // considered obsolete now:  (FIXME: remove them)
 206
 207 #define BEGIN_TYPECHECK \\
 208 bool automatic_typecheck=true;
 209
 210 #define TYPECHECK(VAR,TYPE) \\
 211 if (!is_exactly_a<TYPE>(VAR)) { \\
 212         automatic_typecheck=false; \\
 213 } else
 214
 215 #define TYPECHECK_INTEGER(VAR) \\
 216 if (!(VAR).info(GiNaC::info_flags::integer)) { \\
 217         automatic_typecheck=false; \\
 218 } else
 219
 220 #define END_TYPECHECK(RV) \\
 221 {} \\
 222 if (!automatic_typecheck) { \\
 223         return RV.hold(); \\
 224 }
 225
 226 namespace GiNaC {
 227
 228 class function;
 229 class symmetry;
 230
 231 typedef ex (* eval_funcp)();
 232 typedef ex (* evalf_funcp)();
 233 typedef ex (* derivative_funcp)();
 234 typedef ex (* series_funcp)();
 235
 236 // the following lines have been generated for max. ${maxargs} parameters
 237 $typedef_eval_funcp
 238 $typedef_evalf_funcp
 239 $typedef_derivative_funcp
 240 $typedef_series_funcp
 241 // end of generated lines
 242
 243 class function_options
 244 {
 245         friend class function;
 246         friend class fderivative;
 247 public:
 248         function_options();
 249         function_options(std::string const & n, std::string const & tn=std::string());
 250         ~function_options();
 251         void initialize(void);
 252         function_options & set_name(std::string const & n, std::string const & tn=std::string());
 253         function_options & latex_name(std::string const & tn);
 254 // the following lines have been generated for max. ${maxargs} parameters
 255 $eval_func_interface
 256 $evalf_func_interface
 257 $derivative_func_interface
 258 $series_func_interface
 259 // end of generated lines
 260         function_options & set_return_type(unsigned rt, unsigned rtt=0);
 261         function_options & do_not_evalf_params(void);
 262         function_options & remember(unsigned size, unsigned assoc_size=0,
 263                                     unsigned strategy=remember_strategies::delete_never);
 264         function_options & overloaded(unsigned o);
 265         function_options & set_symmetry(const symmetry & s);
 266         void test_and_set_nparams(unsigned n);
 267         std::string get_name(void) const { return name; }
 268         unsigned get_nparams(void) const { return nparams; }
 269         bool has_derivative(void) const { return derivative_f != NULL; }
 270
 271 protected:
 272         std::string name;
 273         std::string TeX_name;
 274
 275         unsigned nparams;
 276
 277         eval_funcp eval_f;
 278         evalf_funcp evalf_f;
 279         derivative_funcp derivative_f;
 280         series_funcp series_f;
 281
 282         bool evalf_params_first;
 283
 284         bool use_return_type;
 285         unsigned return_type;
 286         unsigned return_type_tinfo;
 287
 288         bool use_remember;
 289         unsigned remember_size;
 290         unsigned remember_assoc_size;
 291         unsigned remember_strategy;
 292
 293         unsigned functions_with_same_name;
 294
 295         ex symtree;
 296 };
 297
 298 /** The class function is used to implement builtin functions like sin, cos...
 299         and user defined functions */
 300 class function : public exprseq
 301 {
 302         GINAC_DECLARE_REGISTERED_CLASS(function, exprseq)
 303
 304         // CINT has a linking problem
 305 #ifndef __MAKECINT__
 306         friend void ginsh_get_ginac_functions(void);
 307 #endif // def __MAKECINT__
 308
 309         friend class remember_table_entry;
 310         // friend class remember_table_list;
 311         // friend class remember_table;
 312
 313 // member functions
 314
 315         // other ctors
 316 public:
 317         function(unsigned ser);
 318         // the following lines have been generated for max. ${maxargs} parameters
 319 $constructors_interface
 320         // end of generated lines
 321         function(unsigned ser, const exprseq & es);
 322         function(unsigned ser, const exvector & v, bool discardable = false);
 323         function(unsigned ser, exvector * vp); // vp will be deleted
 324
 325         // functions overriding virtual functions from base classes
 326 public:
 327         void print(const print_context & c, unsigned level = 0) const;
 328         unsigned precedence(void) const {return 70;}
 329         int degree(const ex & s) const;
 330         int ldegree(const ex & s) const;
 331         ex coeff(const ex & s, int n = 1) const;
 332         ex expand(unsigned options=0) const;
 333         ex eval(int level=0) const;
 334         ex evalf(int level=0) const;
 335         unsigned calchash(void) const;
 336         ex series(const relational & r, int order, unsigned options = 0) const;
 337         ex thisexprseq(const exvector & v) const;
 338         ex thisexprseq(exvector * vp) const;
 339 protected:
 340         ex derivative(const symbol & s) const;
 341         bool is_equal_same_type(const basic & other) const;
 342         bool match_same_type(const basic & other) const;
 343         unsigned return_type(void) const;
 344         unsigned return_type_tinfo(void) const;
 345
 346         // new virtual functions which can be overridden by derived classes
 347         // none
 348
 349         // non-virtual functions in this class
 350 protected:
 351         ex pderivative(unsigned diff_param) const; // partial differentiation
 352         static std::vector<function_options> & registered_functions(void);
 353         bool lookup_remember_table(ex & result) const;
 354         void store_remember_table(ex const & result) const;
 355 public:
 356         static unsigned register_new(function_options const & opt);
 357         static unsigned find_function(const std::string &name, unsigned nparams);
 358         unsigned get_serial(void) const {return serial;}
 359         std::string get_name(void) const;
 360
 361 // member variables
 362
 363 protected:
 364         unsigned serial;
 365 };
 366
 367 // utility functions/macros
 368 /** Return the object of type function handled by an ex.
 369  *  This is unsafe: you need to check the type first. */
 370 inline const function &ex_to_function(const ex &e)
 371 {
 372         return static_cast<const function &>(*e.bp);
 373 }
 374
 375 /** Specialization of is_exactly_a<function>(obj) for objects of type function. */
 376 template<> inline bool is_exactly_a<function>(const basic & obj)
 377 {
 378         return obj.tinfo()==TINFO_function;
 379 }
 380
 381 #define is_ex_the_function(OBJ, FUNCNAME) \\
 382         (is_exactly_a<function>(OBJ) && static_cast<GiNaC::function *>(OBJ.bp)->get_serial() == function_index_##FUNCNAME)
 383
 384 } // namespace GiNaC
 385
 386 #endif // ndef __GINAC_FUNCTION_H__
 387
 388 END_OF_INTERFACE
 389
 390 $implementation=<<END_OF_IMPLEMENTATION;
 391 /** \@file function.cpp
 392  *
 393  *  Implementation of class of symbolic functions. */
 394
 395 /*
 396  *  This file was generated automatically by function.pl.
 397  *  Please do not modify it directly, edit the perl script instead!
 398  *  function.pl options: \$maxargs=${maxargs}
 399  *
 400  *  GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
 401  *
 402  *  This program is free software; you can redistribute it and/or modify
 403  *  it under the terms of the GNU General Public License as published by
 404  *  the Free Software Foundation; either version 2 of the License, or
 405  *  (at your option) any later version.
 406  *
 407  *  This program is distributed in the hope that it will be useful,
 408  *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 409  *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 410  *  GNU General Public License for more details.
 411  *
 412  *  You should have received a copy of the GNU General Public License
 413  *  along with this program; if not, write to the Free Software
 414  *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 415  */
 416
 417 #include <string>
 418 #include <stdexcept>
 419 #include <list>
 420
 421 #include "function.h"
 422 #include "fderivative.h"
 423 #include "ex.h"
 424 #include "lst.h"
 425 #include "symmetry.h"
 426 #include "print.h"
 427 #include "archive.h"
 428 #include "inifcns.h"
 429 #include "tostring.h"
 430 #include "utils.h"
 431 #include "debugmsg.h"
 432 #include "remember.h"
 433
 434 namespace GiNaC {
 435
 436 //////////
 437 // helper class function_options
 438 //////////
 439
 440 function_options::function_options()
 441 {
 442         initialize();
 443 }
 444
 445 function_options::function_options(std::string const & n, std::string const & tn)
 446 {
 447         initialize();
 448         set_name(n,tn);
 449 }
 450
 451 function_options::~function_options()
 452 {
 453         // nothing to clean up at the moment
 454 }
 455
 456 void function_options::initialize(void)
 457 {
 458         set_name("unnamed_function","\\\\mbox{unnamed}");
 459         nparams = 0;
 460         eval_f = evalf_f = derivative_f = series_f = 0;
 461         evalf_params_first = true;
 462         use_return_type = false;
 463         use_remember = false;
 464         functions_with_same_name = 1;
 465         symtree = 0;
 466 }
 467
 468 function_options & function_options::set_name(std::string const & n,
 469                                               std::string const & tn)
 470 {
 471         name=n;
 472         if (tn==std::string())
 473                 TeX_name = "\\\\mbox{"+name+"}";
 474         else
 475                 TeX_name = tn;
 476         return *this;
 477 }
 478
 479 function_options & function_options::latex_name(std::string const & tn)
 480 {
 481         TeX_name=tn;
 482         return *this;
 483 }
 484
 485 // the following lines have been generated for max. ${maxargs} parameters
 486 $eval_func_implementation
 487 $evalf_func_implementation
 488 $derivative_func_implementation
 489 $series_func_implementation
 490 // end of generated lines
 491
 492 function_options & function_options::set_return_type(unsigned rt, unsigned rtt)
 493 {
 494         use_return_type = true;
 495         return_type = rt;
 496         return_type_tinfo = rtt;
 497         return *this;
 498 }
 499
 500 function_options & function_options::do_not_evalf_params(void)
 501 {
 502         evalf_params_first = false;
 503         return *this;
 504 }
 505
 506 function_options & function_options::remember(unsigned size,
 507                                               unsigned assoc_size,
 508                                               unsigned strategy)
 509 {
 510         use_remember = true;
 511         remember_size = size;
 512         remember_assoc_size = assoc_size;
 513         remember_strategy = strategy;
 514         return *this;
 515 }
 516
 517 function_options & function_options::overloaded(unsigned o)
 518 {
 519         functions_with_same_name = o;
 520         return *this;
 521 }
 522
 523 function_options & function_options::set_symmetry(const symmetry & s)
 524 {
 525         symtree = s;
 526         return *this;
 527 }
 528
 529 void function_options::test_and_set_nparams(unsigned n)
 530 {
 531         if (nparams==0) {
 532                 nparams = n;
 533         } else if (nparams!=n) {
 534                 // we do not throw an exception here because this code is
 535                 // usually executed before main(), so the exception could not
 536                 // caught anyhow
 537                 std::cerr << "WARNING: number of parameters ("
 538                           << n << ") differs from number set before ("
 539                           << nparams << ")" << std::endl;
 540         }
 541 }
 542
 543 GINAC_IMPLEMENT_REGISTERED_CLASS(function, exprseq)
 544
 545 //////////
 546 // default ctor, dtor, copy ctor assignment operator and helpers
 547 //////////
 548
 549 // public
 550
 551 function::function() : serial(0)
 552 {
 553         debugmsg("function default ctor",LOGLEVEL_CONSTRUCT);
 554         tinfo_key = TINFO_function;
 555 }
 556
 557 // protected
 558
 559 void function::copy(const function & other)
 560 {
 561         inherited::copy(other);
 562         serial = other.serial;
 563 }
 564
 565 void function::destroy(bool call_parent)
 566 {
 567         if (call_parent)
 568                 inherited::destroy(call_parent);
 569 }
 570
 571 //////////
 572 // other ctors
 573 //////////
 574
 575 // public
 576
 577 function::function(unsigned ser) : serial(ser)
 578 {
 579         debugmsg("function ctor from unsigned",LOGLEVEL_CONSTRUCT);
 580         tinfo_key = TINFO_function;
 581 }
 582
 583 // the following lines have been generated for max. ${maxargs} parameters
 584 $constructors_implementation
 585 // end of generated lines
 586
 587 function::function(unsigned ser, const exprseq & es) : exprseq(es), serial(ser)
 588 {
 589         debugmsg("function ctor from unsigned,exprseq",LOGLEVEL_CONSTRUCT);
 590         tinfo_key = TINFO_function;
 591 }
 592
 593 function::function(unsigned ser, const exvector & v, bool discardable)
 594   : exprseq(v,discardable), serial(ser)
 595 {
 596         debugmsg("function ctor from string,exvector,bool",LOGLEVEL_CONSTRUCT);
 597         tinfo_key = TINFO_function;
 598 }
 599
 600 function::function(unsigned ser, exvector * vp)
 601   : exprseq(vp), serial(ser)
 602 {
 603         debugmsg("function ctor from unsigned,exvector *",LOGLEVEL_CONSTRUCT);
 604         tinfo_key = TINFO_function;
 605 }
 606
 607 //////////
 608 // archiving
 609 //////////
 610
 611 /** Construct object from archive_node. */
 612 function::function(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
 613 {
 614         debugmsg("function ctor from archive_node", LOGLEVEL_CONSTRUCT);
 615
 616         // Find serial number by function name
 617         std::string s;
 618         if (n.find_string("name", s)) {
 619                 unsigned int ser = 0;
 620                 std::vector<function_options>::const_iterator i = registered_functions().begin(), iend = registered_functions().end();
 621                 while (i != iend) {
 622                         if (s == i->name) {
 623                                 serial = ser;
 624                                 return;
 625                         }
 626                         ++i; ++ser;
 627                 }
 628                 throw (std::runtime_error("unknown function '" + s + "' in archive"));
 629         } else
 630                 throw (std::runtime_error("unnamed function in archive"));
 631 }
 632
 633 /** Unarchive the object. */
 634 ex function::unarchive(const archive_node &n, const lst &sym_lst)
 635 {
 636         return (new function(n, sym_lst))->setflag(status_flags::dynallocated);
 637 }
 638
 639 /** Archive the object. */
 640 void function::archive(archive_node &n) const
 641 {
 642         inherited::archive(n);
 643         GINAC_ASSERT(serial < registered_functions().size());
 644         n.add_string("name", registered_functions()[serial].name);
 645 }
 646
 647 //////////
 648 // functions overriding virtual functions from base classes
 649 //////////
 650
 651 // public
 652
 653 void function::print(const print_context & c, unsigned level) const
 654 {
 655         debugmsg("function print", LOGLEVEL_PRINT);
 656
 657         GINAC_ASSERT(serial<registered_functions().size());
 658
 659         if (is_of_type(c, print_tree)) {
 660
 661                 c.s << std::string(level, ' ') << class_name() << " "
 662                     << registered_functions()[serial].name
 663                     << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
 664                     << ", nops=" << nops()
 665                     << std::endl;
 666                 unsigned delta_indent = static_cast<const print_tree &>(c).delta_indent;
 667                 for (unsigned i=0; i<seq.size(); ++i)
 668                         seq[i].print(c, level + delta_indent);
 669                 c.s << std::string(level + delta_indent, ' ') << "=====" << std::endl;
 670
 671         } else if (is_of_type(c, print_csrc)) {
 672
 673                 // Print function name in lowercase
 674                 std::string lname = registered_functions()[serial].name;
 675                 unsigned num = lname.size();
 676                 for (unsigned i=0; i<num; i++)
 677                         lname[i] = tolower(lname[i]);
 678                 c.s << lname << "(";
 679
 680                 // Print arguments, separated by commas
 681                 exvector::const_iterator it = seq.begin(), itend = seq.end();
 682                 while (it != itend) {
 683                         it->print(c);
 684                         ++it;
 685                         if (it != itend)
 686                                 c.s << ",";
 687                 }
 688                 c.s << ")";
 689
 690         } else if (is_of_type(c, print_latex)) {
 691                 c.s << registered_functions()[serial].TeX_name;
 692                 printseq(c, '(', ',', ')', exprseq::precedence(), function::precedence());
 693         } else {
 694                 c.s << registered_functions()[serial].name;
 695                 printseq(c, '(', ',', ')', exprseq::precedence(), function::precedence());
 696         }
 697 }
 698
 699 ex function::expand(unsigned options) const
 700 {
 701         // Only expand arguments when asked to do so
 702         if (options & expand_options::expand_function_args)
 703                 return inherited::expand(options);
 704         else
 705                 return (options == 0) ? setflag(status_flags::expanded) : *this;
 706 }
 707
 708 int function::degree(const ex & s) const
 709 {
 710         return is_equal(*s.bp) ? 1 : 0;
 711 }
 712
 713 int function::ldegree(const ex & s) const
 714 {
 715         return is_equal(*s.bp) ? 1 : 0;
 716 }
 717
 718 ex function::coeff(const ex & s, int n) const
 719 {
 720         if (is_equal(*s.bp))
 721                 return n==1 ? _ex1() : _ex0();
 722         else
 723                 return n==0 ? ex(*this) : _ex0();
 724 }
 725
 726 ex function::eval(int level) const
 727 {
 728         GINAC_ASSERT(serial<registered_functions().size());
 729
 730         if (level>1) {
 731                 // first evaluate children, then we will end up here again
 732                 return function(serial,evalchildren(level));
 733         }
 734
 735         const function_options &opt = registered_functions()[serial];
 736
 737         // Canonicalize argument order according to the symmetry properties
 738         if (seq.size() > 1 && !(opt.symtree.is_zero())) {
 739                 exvector v = seq;
 740                 GINAC_ASSERT(is_a<symmetry>(opt.symtree));
 741                 int sig = canonicalize(v.begin(), ex_to<symmetry>(opt.symtree));
 742                 if (sig != INT_MAX) {
 743                         // Something has changed while sorting arguments, more evaluations later
 744                         if (sig == 0)
 745                                 return _ex0();
 746                         return ex(sig) * thisexprseq(v);
 747                 }
 748         }
 749
 750         if (opt.eval_f==0) {
 751                 return this->hold();
 752         }
 753
 754         bool use_remember = opt.use_remember;
 755         ex eval_result;
 756         if (use_remember && lookup_remember_table(eval_result)) {
 757                 return eval_result;
 758         }
 759
 760         switch (opt.nparams) {
 761                 // the following lines have been generated for max. ${maxargs} parameters
 762 ${eval_switch_statement}
 763                 // end of generated lines
 764         default:
 765                 throw(std::logic_error("function::eval(): invalid nparams"));
 766         }
 767         if (use_remember) {
 768                 store_remember_table(eval_result);
 769         }
 770         return eval_result;
 771 }
 772
 773 ex function::evalf(int level) const
 774 {
 775         GINAC_ASSERT(serial<registered_functions().size());
 776
 777         // Evaluate children first
 778         exvector eseq;
 779         if (level == 1)
 780                 eseq = seq;
 781         else if (level == -max_recursion_level)
 782                 throw(std::runtime_error("max recursion level reached"));
 783         else
 784                 eseq.reserve(seq.size());
 785         --level;
 786         exvector::const_iterator it = seq.begin(), itend = seq.end();
 787         while (it != itend) {
 788                 eseq.push_back(it->evalf(level));
 789                 ++it;
 790         }
 791
 792         if (registered_functions()[serial].evalf_f==0) {
 793                 return function(serial,eseq).hold();
 794         }
 795         switch (registered_functions()[serial].nparams) {
 796                 // the following lines have been generated for max. ${maxargs} parameters
 797 ${evalf_switch_statement}
 798                 // end of generated lines
 799         }
 800         throw(std::logic_error("function::evalf(): invalid nparams"));
 801 }
 802
 803 unsigned function::calchash(void) const
 804 {
 805         unsigned v = golden_ratio_hash(golden_ratio_hash(tinfo()) ^ serial);
 806         for (unsigned i=0; i<nops(); i++) {
 807                 v = rotate_left_31(v);
 808                 v ^= this->op(i).gethash();
 809         }
 810         v &= 0x7FFFFFFFU;
 811         if (flags & status_flags::evaluated) {
 812                 setflag(status_flags::hash_calculated);
 813                 hashvalue = v;
 814         }
 815         return v;
 816 }
 817
 818 ex function::thisexprseq(const exvector & v) const
 819 {
 820         return function(serial,v);
 821 }
 822
 823 ex function::thisexprseq(exvector * vp) const
 824 {
 825         return function(serial,vp);
 826 }
 827
 828 /** Implementation of ex::series for functions.
 829  *  \@see ex::series */
 830 ex function::series(const relational & r, int order, unsigned options) const
 831 {
 832         GINAC_ASSERT(serial<registered_functions().size());
 833
 834         if (registered_functions()[serial].series_f==0) {
 835                 return basic::series(r, order);
 836         }
 837         ex res;
 838         switch (registered_functions()[serial].nparams) {
 839                 // the following lines have been generated for max. ${maxargs} parameters
 840 ${series_switch_statement}
 841                 // end of generated lines
 842         }
 843         throw(std::logic_error("function::series(): invalid nparams"));
 844 }
 845
 846 // protected
 847
 848 /** Implementation of ex::diff() for functions. It applies the chain rule,
 849  *  except for the Order term function.
 850  *  \@see ex::diff */
 851 ex function::derivative(const symbol & s) const
 852 {
 853         ex result;
 854
 855         if (serial == function_index_Order) {
 856                 // Order Term function only differentiates the argument
 857                 return Order(seq[0].diff(s));
 858         } else {
 859                 // Chain rule
 860                 ex arg_diff;
 861                 unsigned num = seq.size();
 862                 for (unsigned i=0; i<num; i++) {
 863                         arg_diff = seq[i].diff(s);
 864                         // We apply the chain rule only when it makes sense.  This is not
 865                         // just for performance reasons but also to allow functions to
 866                         // throw when differentiated with respect to one of its arguments
 867                         // without running into trouble with our automatic full
 868                         // differentiation:
 869                         if (!arg_diff.is_zero())
 870                                 result += pderivative(i)*arg_diff;
 871                 }
 872         }
 873         return result;
 874 }
 875
 876 int function::compare_same_type(const basic & other) const
 877 {
 878         GINAC_ASSERT(is_of_type(other, function));
 879         const function & o = static_cast<const function &>(other);
 880
 881         if (serial != o.serial)
 882                 return serial < o.serial ? -1 : 1;
 883         else
 884                 return exprseq::compare_same_type(o);
 885 }
 886
 887 bool function::is_equal_same_type(const basic & other) const
 888 {
 889         GINAC_ASSERT(is_of_type(other, function));
 890         const function & o = static_cast<const function &>(other);
 891
 892         if (serial != o.serial)
 893                 return false;
 894         else
 895                 return exprseq::is_equal_same_type(o);
 896 }
 897
 898 bool function::match_same_type(const basic & other) const
 899 {
 900         GINAC_ASSERT(is_of_type(other, function));
 901         const function & o = static_cast<const function &>(other);
 902
 903         return serial == o.serial;
 904 }
 905
 906 unsigned function::return_type(void) const
 907 {
 908         if (seq.empty())
 909                 return return_types::commutative;
 910         else
 911                 return seq.begin()->return_type();
 912 }
 913
 914 unsigned function::return_type_tinfo(void) const
 915 {
 916         if (seq.empty())
 917                 return tinfo_key;
 918         else
 919                 return seq.begin()->return_type_tinfo();
 920 }
 921
 922 //////////
 923 // new virtual functions which can be overridden by derived classes
 924 //////////
 925
 926 // none
 927
 928 //////////
 929 // non-virtual functions in this class
 930 //////////
 931
 932 // protected
 933
 934 ex function::pderivative(unsigned diff_param) const // partial differentiation
 935 {
 936         GINAC_ASSERT(serial<registered_functions().size());
 937
 938         // No derivative defined? Then return abstract derivative object
 939         if (registered_functions()[serial].derivative_f == NULL)
 940                 return fderivative(serial, diff_param, seq);
 941
 942         switch (registered_functions()[serial].nparams) {
 943                 // the following lines have been generated for max. ${maxargs} parameters
 944 ${diff_switch_statement}
 945                 // end of generated lines
 946         }
 947         throw(std::logic_error("function::pderivative(): no diff function defined"));
 948 }
 949
 950 std::vector<function_options> & function::registered_functions(void)
 951 {
 952         static std::vector<function_options> * rf = new std::vector<function_options>;
 953         return *rf;
 954 }
 955
 956 bool function::lookup_remember_table(ex & result) const
 957 {
 958         return remember_table::remember_tables()[serial].lookup_entry(*this,result);
 959 }
 960
 961 void function::store_remember_table(ex const & result) const
 962 {
 963         remember_table::remember_tables()[serial].add_entry(*this,result);
 964 }
 965
 966 // public
 967
 968 unsigned function::register_new(function_options const & opt)
 969 {
 970         unsigned same_name = 0;
 971         for (unsigned i=0; i<registered_functions().size(); ++i) {
 972                 if (registered_functions()[i].name==opt.name) {
 973                         ++same_name;
 974                 }
 975         }
 976         if (same_name>=opt.functions_with_same_name) {
 977                 // we do not throw an exception here because this code is
 978                 // usually executed before main(), so the exception could not
 979                 // caught anyhow
 980                 std::cerr << "WARNING: function name " << opt.name
 981                           << " already in use!" << std::endl;
 982         }
 983         registered_functions().push_back(opt);
 984         if (opt.use_remember) {
 985                 remember_table::remember_tables().
 986                         push_back(remember_table(opt.remember_size,
 987                                                  opt.remember_assoc_size,
 988                                                  opt.remember_strategy));
 989         } else {
 990                 remember_table::remember_tables().push_back(remember_table());
 991         }
 992         return registered_functions().size()-1;
 993 }
 994
 995 /** Find serial number of function by name and number of parameters.
 996  *  Throws exception if function was not found. */
 997 unsigned function::find_function(const std::string &name, unsigned nparams)
 998 {
 999         std::vector<function_options>::const_iterator i = function::registered_functions().begin(), end = function::registered_functions().end();
1000         unsigned serial = 0;
1001         while (i != end) {
1002                 if (i->get_name() == name && i->get_nparams() == nparams)
1003                         return serial;
1004                 ++i;
1005                 ++serial;
1006         }
1007         throw (std::runtime_error("no function '" + name + "' with " + ToString(nparams) + " parameters defined"));
1008 }
1009
1010 /** Return the print name of the function. */
1011 std::string function::get_name(void) const
1012 {
1013         GINAC_ASSERT(serial<registered_functions().size());
1014         return registered_functions()[serial].name;
1015 }
1016
1017 } // namespace GiNaC
1018
1019 END_OF_IMPLEMENTATION
1020
1021 print "Creating interface file function.h...";
1022 open OUT,">function.h" or die "cannot open function.h";
1023 print OUT $interface;
1024 close OUT;
1025 print "ok.\n";
1026
1027 print "Creating implementation file function.cpp...";
1028 open OUT,">function.cpp" or die "cannot open function.cpp";
1029 print OUT $implementation;
1030 close OUT;
1031 print "ok.\n";
1032
1033 print "done.\n";