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         tinfo_key = TINFO_function;
  84 }
  85 END_OF_CONSTRUCTORS_IMPLEMENTATION
  86
  87 $eval_switch_statement=generate(
  88         <<'END_OF_EVAL_SWITCH_STATEMENT','seq[${N}-1]','','');
  89         case ${N}:
  90                 eval_result = ((eval_funcp_${N})(registered_functions()[serial].eval_f))(${SEQ1});
  91                 break;
  92 END_OF_EVAL_SWITCH_STATEMENT
  93
  94 $evalf_switch_statement=generate(
  95         <<'END_OF_EVALF_SWITCH_STATEMENT','eseq[${N}-1]','','');
  96         case ${N}:
  97                 return ((evalf_funcp_${N})(registered_functions()[serial].evalf_f))(${SEQ1});
  98 END_OF_EVALF_SWITCH_STATEMENT
  99
 100 $diff_switch_statement=generate(
 101         <<'END_OF_DIFF_SWITCH_STATEMENT','seq[${N}-1]','','');
 102         case ${N}:
 103                 return ((derivative_funcp_${N})(registered_functions()[serial].derivative_f))(${SEQ1},diff_param);
 104 END_OF_DIFF_SWITCH_STATEMENT
 105
 106 $series_switch_statement=generate(
 107         <<'END_OF_SERIES_SWITCH_STATEMENT','seq[${N}-1]','','');
 108         case ${N}:
 109                 try {
 110                         res = ((series_funcp_${N})(registered_functions()[serial].series_f))(${SEQ1},r,order,options);
 111                 } catch (do_taylor) {
 112                         res = basic::series(r, order, options);
 113                 }
 114                 return res;
 115 END_OF_SERIES_SWITCH_STATEMENT
 116
 117 $eval_func_implementation=generate(
 118         <<'END_OF_EVAL_FUNC_IMPLEMENTATION','','','');
 119 function_options & function_options::eval_func(eval_funcp_${N} e)
 120 {
 121         test_and_set_nparams(${N});
 122         eval_f = eval_funcp(e);
 123         return *this;
 124 }
 125 END_OF_EVAL_FUNC_IMPLEMENTATION
 126
 127 $evalf_func_implementation=generate(
 128         <<'END_OF_EVALF_FUNC_IMPLEMENTATION','','','');
 129 function_options & function_options::evalf_func(evalf_funcp_${N} ef)
 130 {
 131         test_and_set_nparams(${N});
 132         evalf_f = evalf_funcp(ef);
 133         return *this;
 134 }
 135 END_OF_EVALF_FUNC_IMPLEMENTATION
 136
 137 $derivative_func_implementation=generate(
 138         <<'END_OF_DERIVATIVE_FUNC_IMPLEMENTATION','','','');
 139 function_options & function_options::derivative_func(derivative_funcp_${N} d)
 140 {
 141         test_and_set_nparams(${N});
 142         derivative_f = derivative_funcp(d);
 143         return *this;
 144 }
 145 END_OF_DERIVATIVE_FUNC_IMPLEMENTATION
 146
 147 $series_func_implementation=generate(
 148         <<'END_OF_SERIES_FUNC_IMPLEMENTATION','','','');
 149 function_options & function_options::series_func(series_funcp_${N} s)
 150 {
 151         test_and_set_nparams(${N});
 152         series_f = series_funcp(s);
 153         return *this;
 154 }
 155 END_OF_SERIES_FUNC_IMPLEMENTATION
 156
 157 $interface=<<END_OF_INTERFACE;
 158 /** \@file function.h
 159  *
 160  *  Interface to class of symbolic functions. */
 161
 162 /*
 163  *  This file was generated automatically by function.pl.
 164  *  Please do not modify it directly, edit the perl script instead!
 165  *  function.pl options: \$maxargs=${maxargs}
 166  *
 167  *  GiNaC Copyright (C) 1999-2003 Johannes Gutenberg University Mainz, Germany
 168  *
 169  *  This program is free software; you can redistribute it and/or modify
 170  *  it under the terms of the GNU General Public License as published by
 171  *  the Free Software Foundation; either version 2 of the License, or
 172  *  (at your option) any later version.
 173  *
 174  *  This program is distributed in the hope that it will be useful,
 175  *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 176  *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 177  *  GNU General Public License for more details.
 178  *
 179  *  You should have received a copy of the GNU General Public License
 180  *  along with this program; if not, write to the Free Software
 181  *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 182  */
 183
 184 #ifndef __GINAC_FUNCTION_H__
 185 #define __GINAC_FUNCTION_H__
 186
 187 #include <string>
 188 #include <vector>
 189
 190 // CINT needs <algorithm> to work properly with <vector>
 191 #include <algorithm>
 192
 193 #include "exprseq.h"
 194
 195 // the following lines have been generated for max. ${maxargs} parameters
 196 $declare_function_macro
 197 // end of generated lines
 198
 199 #define REGISTER_FUNCTION(NAME,OPT) \\
 200 const unsigned function_index_##NAME= \\
 201         GiNaC::function::register_new(GiNaC::function_options(#NAME).OPT);
 202
 203 namespace GiNaC {
 204
 205 class function;
 206 class symmetry;
 207
 208 typedef ex (* eval_funcp)();
 209 typedef ex (* evalf_funcp)();
 210 typedef ex (* derivative_funcp)();
 211 typedef ex (* series_funcp)();
 212
 213 // the following lines have been generated for max. ${maxargs} parameters
 214 $typedef_eval_funcp
 215 $typedef_evalf_funcp
 216 $typedef_derivative_funcp
 217 $typedef_series_funcp
 218 // end of generated lines
 219
 220 // Alternatively, an exvector may be passed into the static function, instead
 221 // of individual ex objects.  Then, the number of arguments is not limited.
 222 typedef ex (* eval_funcp_exvector)(const exvector &);
 223 typedef ex (* evalf_funcp_exvector)(const exvector &);
 224 typedef ex (* derivative_funcp_exvector)(const exvector &, unsigned);
 225 typedef ex (* series_funcp_exvector)(const exvector &, const relational &, int, unsigned);
 226
 227 class function_options
 228 {
 229         friend class function;
 230         friend class fderivative;
 231 public:
 232         function_options();
 233         function_options(std::string const & n, std::string const & tn=std::string());
 234         ~function_options();
 235         void initialize(void);
 236         function_options & set_name(std::string const & n, std::string const & tn=std::string());
 237         function_options & latex_name(std::string const & tn);
 238 // the following lines have been generated for max. ${maxargs} parameters
 239 $eval_func_interface
 240 $evalf_func_interface
 241 $derivative_func_interface
 242 $series_func_interface
 243 // end of generated lines
 244         function_options & eval_func(eval_funcp_exvector e);
 245         function_options & evalf_func(evalf_funcp_exvector ef);
 246         function_options & derivative_func(derivative_funcp_exvector d);
 247         function_options & series_func(series_funcp_exvector s);
 248
 249         function_options & set_return_type(unsigned rt, unsigned rtt=0);
 250         function_options & do_not_evalf_params(void);
 251         function_options & remember(unsigned size, unsigned assoc_size=0,
 252                                     unsigned strategy=remember_strategies::delete_never);
 253         function_options & overloaded(unsigned o);
 254         function_options & set_symmetry(const symmetry & s);
 255         void test_and_set_nparams(unsigned n);
 256         std::string get_name(void) const { return name; }
 257         unsigned get_nparams(void) const { return nparams; }
 258         bool has_derivative(void) const { return derivative_f != NULL; }
 259
 260 protected:
 261         std::string name;
 262         std::string TeX_name;
 263
 264         unsigned nparams;
 265
 266         eval_funcp eval_f;
 267         evalf_funcp evalf_f;
 268         derivative_funcp derivative_f;
 269         series_funcp series_f;
 270
 271         bool evalf_params_first;
 272
 273         bool use_return_type;
 274         unsigned return_type;
 275         unsigned return_type_tinfo;
 276
 277         bool use_remember;
 278         unsigned remember_size;
 279         unsigned remember_assoc_size;
 280         unsigned remember_strategy;
 281
 282         bool eval_use_exvector_args;
 283         bool evalf_use_exvector_args;
 284         bool derivative_use_exvector_args;
 285         bool series_use_exvector_args;
 286
 287         unsigned functions_with_same_name;
 288
 289         ex symtree;
 290 };
 291
 292 /** The class function is used to implement builtin functions like sin, cos...
 293         and user defined functions */
 294 class function : public exprseq
 295 {
 296         GINAC_DECLARE_REGISTERED_CLASS(function, exprseq)
 297
 298         // CINT has a linking problem
 299 #ifndef __MAKECINT__
 300         friend void ginsh_get_ginac_functions(void);
 301 #endif // def __MAKECINT__
 302
 303         friend class remember_table_entry;
 304         // friend class remember_table_list;
 305         // friend class remember_table;
 306
 307 // member functions
 308
 309         // other ctors
 310 public:
 311         function(unsigned ser);
 312         // the following lines have been generated for max. ${maxargs} parameters
 313 $constructors_interface
 314         // end of generated lines
 315         function(unsigned ser, const exprseq & es);
 316         function(unsigned ser, const exvector & v, bool discardable = false);
 317         function(unsigned ser, exvector * vp); // vp will be deleted
 318
 319         // functions overriding virtual functions from base classes
 320 public:
 321         void print(const print_context & c, unsigned level = 0) const;
 322         unsigned precedence(void) const {return 70;}
 323         ex expand(unsigned options=0) const;
 324         ex eval(int level=0) const;
 325         ex evalf(int level=0) const;
 326         unsigned calchash(void) const;
 327         ex series(const relational & r, int order, unsigned options = 0) const;
 328         ex thisexprseq(const exvector & v) const;
 329         ex thisexprseq(exvector * vp) const;
 330 protected:
 331         ex derivative(const symbol & s) const;
 332         bool is_equal_same_type(const basic & other) const;
 333         bool match_same_type(const basic & other) const;
 334         unsigned return_type(void) const;
 335         unsigned return_type_tinfo(void) const;
 336
 337         // new virtual functions which can be overridden by derived classes
 338         // none
 339
 340         // non-virtual functions in this class
 341 protected:
 342         ex pderivative(unsigned diff_param) const; // partial differentiation
 343         static std::vector<function_options> & registered_functions(void);
 344         bool lookup_remember_table(ex & result) const;
 345         void store_remember_table(ex const & result) const;
 346 public:
 347         static unsigned register_new(function_options const & opt);
 348         static unsigned current_serial;
 349         static unsigned find_function(const std::string &name, unsigned nparams);
 350         unsigned get_serial(void) const {return serial;}
 351         std::string get_name(void) const;
 352
 353 // member variables
 354
 355 protected:
 356         unsigned serial;
 357 };
 358
 359 // utility functions/macros
 360
 361 /** Specialization of is_exactly_a<function>(obj) for objects of type function. */
 362 template<> inline bool is_exactly_a<function>(const basic & obj)
 363 {
 364         return obj.tinfo()==TINFO_function;
 365 }
 366
 367 #define is_ex_the_function(OBJ, FUNCNAME) \\
 368         (GiNaC::is_exactly_a<GiNaC::function>(OBJ) && GiNaC::ex_to<GiNaC::function>(OBJ).get_serial() == function_index_##FUNCNAME)
 369
 370 } // namespace GiNaC
 371
 372 #endif // ndef __GINAC_FUNCTION_H__
 373
 374 END_OF_INTERFACE
 375
 376 $implementation=<<END_OF_IMPLEMENTATION;
 377 /** \@file function.cpp
 378  *
 379  *  Implementation of class of symbolic functions. */
 380
 381 /*
 382  *  This file was generated automatically by function.pl.
 383  *  Please do not modify it directly, edit the perl script instead!
 384  *  function.pl options: \$maxargs=${maxargs}
 385  *
 386  *  GiNaC Copyright (C) 1999-2003 Johannes Gutenberg University Mainz, Germany
 387  *
 388  *  This program is free software; you can redistribute it and/or modify
 389  *  it under the terms of the GNU General Public License as published by
 390  *  the Free Software Foundation; either version 2 of the License, or
 391  *  (at your option) any later version.
 392  *
 393  *  This program is distributed in the hope that it will be useful,
 394  *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 395  *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 396  *  GNU General Public License for more details.
 397  *
 398  *  You should have received a copy of the GNU General Public License
 399  *  along with this program; if not, write to the Free Software
 400  *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 401  */
 402
 403 #include <iostream>
 404 #include <string>
 405 #include <stdexcept>
 406 #include <list>
 407
 408 #include "function.h"
 409 #include "fderivative.h"
 410 #include "ex.h"
 411 #include "lst.h"
 412 #include "symmetry.h"
 413 #include "print.h"
 414 #include "archive.h"
 415 #include "inifcns.h"
 416 #include "tostring.h"
 417 #include "utils.h"
 418 #include "remember.h"
 419
 420 namespace GiNaC {
 421
 422 //////////
 423 // helper class function_options
 424 //////////
 425
 426 function_options::function_options()
 427 {
 428         initialize();
 429 }
 430
 431 function_options::function_options(std::string const & n, std::string const & tn)
 432 {
 433         initialize();
 434         set_name(n,tn);
 435 }
 436
 437 function_options::~function_options()
 438 {
 439         // nothing to clean up at the moment
 440 }
 441
 442 void function_options::initialize(void)
 443 {
 444         set_name("unnamed_function","\\\\mbox{unnamed}");
 445         nparams = 0;
 446         eval_f = evalf_f = derivative_f = series_f = 0;
 447         evalf_params_first = true;
 448         use_return_type = false;
 449         eval_use_exvector_args = false;
 450         evalf_use_exvector_args = false;
 451         derivative_use_exvector_args = false;
 452         series_use_exvector_args = false;
 453         use_remember = false;
 454         functions_with_same_name = 1;
 455         symtree = 0;
 456 }
 457
 458 function_options & function_options::set_name(std::string const & n,
 459                                               std::string const & tn)
 460 {
 461         name = n;
 462         if (tn==std::string())
 463                 TeX_name = "\\\\mbox{"+name+"}";
 464         else
 465                 TeX_name = tn;
 466         return *this;
 467 }
 468
 469 function_options & function_options::latex_name(std::string const & tn)
 470 {
 471         TeX_name = tn;
 472         return *this;
 473 }
 474
 475 // the following lines have been generated for max. ${maxargs} parameters
 476 $eval_func_implementation
 477 $evalf_func_implementation
 478 $derivative_func_implementation
 479 $series_func_implementation
 480 // end of generated lines
 481
 482 function_options& function_options::eval_func(eval_funcp_exvector e)
 483 {
 484         eval_use_exvector_args = true;
 485         eval_f = eval_funcp(e);
 486         return *this;
 487 }
 488 function_options& function_options::evalf_func(evalf_funcp_exvector ef)
 489 {
 490         evalf_use_exvector_args = true;
 491         evalf_f = evalf_funcp(ef);
 492         return *this;
 493 }
 494 function_options& function_options::derivative_func(derivative_funcp_exvector d)
 495 {
 496         derivative_use_exvector_args = true;
 497         derivative_f = derivative_funcp(d);
 498         return *this;
 499 }
 500 function_options& function_options::series_func(series_funcp_exvector s)
 501 {
 502         series_use_exvector_args = true;
 503         series_f = series_funcp(s);
 504         return *this;
 505 }
 506
 507 function_options & function_options::set_return_type(unsigned rt, unsigned rtt)
 508 {
 509         use_return_type = true;
 510         return_type = rt;
 511         return_type_tinfo = rtt;
 512         return *this;
 513 }
 514
 515 function_options & function_options::do_not_evalf_params(void)
 516 {
 517         evalf_params_first = false;
 518         return *this;
 519 }
 520
 521 function_options & function_options::remember(unsigned size,
 522                                               unsigned assoc_size,
 523                                               unsigned strategy)
 524 {
 525         use_remember = true;
 526         remember_size = size;
 527         remember_assoc_size = assoc_size;
 528         remember_strategy = strategy;
 529         return *this;
 530 }
 531
 532 function_options & function_options::overloaded(unsigned o)
 533 {
 534         functions_with_same_name = o;
 535         return *this;
 536 }
 537
 538 function_options & function_options::set_symmetry(const symmetry & s)
 539 {
 540         symtree = s;
 541         return *this;
 542 }
 543
 544 void function_options::test_and_set_nparams(unsigned n)
 545 {
 546         if (nparams==0) {
 547                 nparams = n;
 548         } else if (nparams!=n) {
 549                 // we do not throw an exception here because this code is
 550                 // usually executed before main(), so the exception could not
 551                 // caught anyhow
 552                 std::cerr << "WARNING: number of parameters ("
 553                           << n << ") differs from number set before ("
 554                           << nparams << ")" << std::endl;
 555         }
 556 }
 557
 558 /** This can be used as a hook for external applications. */
 559 unsigned function::current_serial = 0;
 560
 561
 562 GINAC_IMPLEMENT_REGISTERED_CLASS(function, exprseq)
 563
 564 //////////
 565 // default ctor, dtor, copy ctor, assignment operator and helpers
 566 //////////
 567
 568 // public
 569
 570 function::function() : serial(0)
 571 {
 572         tinfo_key = TINFO_function;
 573 }
 574
 575 // protected
 576
 577 void function::copy(const function & other)
 578 {
 579         inherited::copy(other);
 580         serial = other.serial;
 581 }
 582
 583 void function::destroy(bool call_parent)
 584 {
 585         if (call_parent)
 586                 inherited::destroy(call_parent);
 587 }
 588
 589 //////////
 590 // other ctors
 591 //////////
 592
 593 // public
 594
 595 function::function(unsigned ser) : serial(ser)
 596 {
 597         tinfo_key = TINFO_function;
 598 }
 599
 600 // the following lines have been generated for max. ${maxargs} parameters
 601 $constructors_implementation
 602 // end of generated lines
 603
 604 function::function(unsigned ser, const exprseq & es) : exprseq(es), serial(ser)
 605 {
 606         tinfo_key = TINFO_function;
 607
 608         // Force re-evaluation even if the exprseq was already evaluated
 609         // (the exprseq copy constructor copies the flags)
 610         clearflag(status_flags::evaluated);
 611 }
 612
 613 function::function(unsigned ser, const exvector & v, bool discardable)
 614   : exprseq(v,discardable), serial(ser)
 615 {
 616         tinfo_key = TINFO_function;
 617 }
 618
 619 function::function(unsigned ser, exvector * vp)
 620   : exprseq(vp), serial(ser)
 621 {
 622         tinfo_key = TINFO_function;
 623 }
 624
 625 //////////
 626 // archiving
 627 //////////
 628
 629 /** Construct object from archive_node. */
 630 function::function(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
 631 {
 632         // Find serial number by function name
 633         std::string s;
 634         if (n.find_string("name", s)) {
 635                 unsigned int ser = 0;
 636                 std::vector<function_options>::const_iterator i = registered_functions().begin(), iend = registered_functions().end();
 637                 while (i != iend) {
 638                         if (s == i->name) {
 639                                 serial = ser;
 640                                 return;
 641                         }
 642                         ++i; ++ser;
 643                 }
 644                 throw (std::runtime_error("unknown function '" + s + "' in archive"));
 645         } else
 646                 throw (std::runtime_error("unnamed function in archive"));
 647 }
 648
 649 /** Unarchive the object. */
 650 ex function::unarchive(const archive_node &n, const lst &sym_lst)
 651 {
 652         return (new function(n, sym_lst))->setflag(status_flags::dynallocated);
 653 }
 654
 655 /** Archive the object. */
 656 void function::archive(archive_node &n) const
 657 {
 658         inherited::archive(n);
 659         GINAC_ASSERT(serial < registered_functions().size());
 660         n.add_string("name", registered_functions()[serial].name);
 661 }
 662
 663 //////////
 664 // functions overriding virtual functions from base classes
 665 //////////
 666
 667 // public
 668
 669 void function::print(const print_context & c, unsigned level) const
 670 {
 671         GINAC_ASSERT(serial<registered_functions().size());
 672
 673         if (is_of_type(c, print_tree)) {
 674
 675                 c.s << std::string(level, ' ') << class_name() << " "
 676                     << registered_functions()[serial].name
 677                     << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
 678                     << ", nops=" << nops()
 679                     << std::endl;
 680                 unsigned delta_indent = static_cast<const print_tree &>(c).delta_indent;
 681                 for (unsigned i=0; i<seq.size(); ++i)
 682                         seq[i].print(c, level + delta_indent);
 683                 c.s << std::string(level + delta_indent, ' ') << "=====" << std::endl;
 684
 685         } else if (is_of_type(c, print_csrc)) {
 686
 687                 // Print function name in lowercase
 688                 std::string lname = registered_functions()[serial].name;
 689                 unsigned num = lname.size();
 690                 for (unsigned i=0; i<num; i++)
 691                         lname[i] = tolower(lname[i]);
 692                 c.s << lname << "(";
 693
 694                 // Print arguments, separated by commas
 695                 exvector::const_iterator it = seq.begin(), itend = seq.end();
 696                 while (it != itend) {
 697                         it->print(c);
 698                         ++it;
 699                         if (it != itend)
 700                                 c.s << ",";
 701                 }
 702                 c.s << ")";
 703
 704         } else if (is_of_type(c, print_latex)) {
 705                 c.s << registered_functions()[serial].TeX_name;
 706                 printseq(c, '(', ',', ')', exprseq::precedence(), function::precedence());
 707         } else {
 708                 c.s << registered_functions()[serial].name;
 709                 printseq(c, '(', ',', ')', exprseq::precedence(), function::precedence());
 710         }
 711 }
 712
 713 ex function::expand(unsigned options) const
 714 {
 715         // Only expand arguments when asked to do so
 716         if (options & expand_options::expand_function_args)
 717                 return inherited::expand(options);
 718         else
 719                 return (options == 0) ? setflag(status_flags::expanded) : *this;
 720 }
 721
 722 ex function::eval(int level) const
 723 {
 724         GINAC_ASSERT(serial<registered_functions().size());
 725
 726         if (level>1) {
 727                 // first evaluate children, then we will end up here again
 728                 return function(serial,evalchildren(level));
 729         }
 730
 731         const function_options &opt = registered_functions()[serial];
 732
 733         // Canonicalize argument order according to the symmetry properties
 734         if (seq.size() > 1 && !(opt.symtree.is_zero())) {
 735                 exvector v = seq;
 736                 GINAC_ASSERT(is_a<symmetry>(opt.symtree));
 737                 int sig = canonicalize(v.begin(), ex_to<symmetry>(opt.symtree));
 738                 if (sig != INT_MAX) {
 739                         // Something has changed while sorting arguments, more evaluations later
 740                         if (sig == 0)
 741                                 return _ex0;
 742                         return ex(sig) * thisexprseq(v);
 743                 }
 744         }
 745
 746         if (opt.eval_f==0) {
 747                 return this->hold();
 748         }
 749
 750         bool use_remember = opt.use_remember;
 751         ex eval_result;
 752         if (use_remember && lookup_remember_table(eval_result)) {
 753                 return eval_result;
 754         }
 755         current_serial = serial;
 756         if (registered_functions()[serial].eval_use_exvector_args)
 757                 eval_result = ((eval_funcp_exvector)(registered_functions()[serial].eval_f))(seq);
 758         else
 759         switch (opt.nparams) {
 760                 // the following lines have been generated for max. ${maxargs} parameters
 761 ${eval_switch_statement}
 762                 // end of generated lines
 763         default:
 764                 throw(std::logic_error("function::eval(): invalid nparams"));
 765         }
 766         if (use_remember) {
 767                 store_remember_table(eval_result);
 768         }
 769         return eval_result;
 770 }
 771
 772 ex function::evalf(int level) const
 773 {
 774         GINAC_ASSERT(serial<registered_functions().size());
 775
 776         const function_options &opt = registered_functions()[serial];
 777
 778         // Evaluate children first
 779         exvector eseq;
 780         if (level == 1 || !(opt.evalf_params_first))
 781                 eseq = seq;
 782         else if (level == -max_recursion_level)
 783                 throw(std::runtime_error("max recursion level reached"));
 784         else {
 785                 eseq.reserve(seq.size());
 786                 --level;
 787                 exvector::const_iterator it = seq.begin(), itend = seq.end();
 788                 while (it != itend) {
 789                         eseq.push_back(it->evalf(level));
 790                         ++it;
 791                 }
 792         }
 793
 794         if (opt.evalf_f==0) {
 795                 return function(serial,eseq).hold();
 796         }
 797         current_serial = serial;
 798         if (opt.evalf_use_exvector_args)
 799                 return ((evalf_funcp_exvector)(opt.evalf_f))(seq);
 800         switch (opt.nparams) {
 801                 // the following lines have been generated for max. ${maxargs} parameters
 802 ${evalf_switch_statement}
 803                 // end of generated lines
 804         }
 805         throw(std::logic_error("function::evalf(): invalid nparams"));
 806 }
 807
 808 unsigned function::calchash(void) const
 809 {
 810         unsigned v = golden_ratio_hash(golden_ratio_hash(tinfo()) ^ serial);
 811         for (unsigned i=0; i<nops(); i++) {
 812                 v = rotate_left_31(v);
 813                 v ^= this->op(i).gethash();
 814         }
 815         v &= 0x7FFFFFFFU;
 816         if (flags & status_flags::evaluated) {
 817                 setflag(status_flags::hash_calculated);
 818                 hashvalue = v;
 819         }
 820         return v;
 821 }
 822
 823 ex function::thisexprseq(const exvector & v) const
 824 {
 825         return function(serial,v);
 826 }
 827
 828 ex function::thisexprseq(exvector * vp) const
 829 {
 830         return function(serial,vp);
 831 }
 832
 833 /** Implementation of ex::series for functions.
 834  *  \@see ex::series */
 835 ex function::series(const relational & r, int order, unsigned options) const
 836 {
 837         GINAC_ASSERT(serial<registered_functions().size());
 838
 839         if (registered_functions()[serial].series_f==0) {
 840                 return basic::series(r, order);
 841         }
 842         ex res;
 843         current_serial = serial;
 844         if (registered_functions()[serial].series_use_exvector_args) {
 845                 try {
 846                         res = ((series_funcp_exvector)(registered_functions()[serial].series_f))(seq, r, order, options);
 847                 } catch (do_taylor) {
 848                         res = basic::series(r, order, options);
 849                 }
 850                 return res;
 851         }
 852         switch (registered_functions()[serial].nparams) {
 853                 // the following lines have been generated for max. ${maxargs} parameters
 854 ${series_switch_statement}
 855                 // end of generated lines
 856         }
 857         throw(std::logic_error("function::series(): invalid nparams"));
 858 }
 859
 860 // protected
 861
 862 /** Implementation of ex::diff() for functions. It applies the chain rule,
 863  *  except for the Order term function.
 864  *  \@see ex::diff */
 865 ex function::derivative(const symbol & s) const
 866 {
 867         ex result;
 868
 869         if (serial == function_index_Order) {
 870                 // Order Term function only differentiates the argument
 871                 return Order(seq[0].diff(s));
 872         } else {
 873                 // Chain rule
 874                 ex arg_diff;
 875                 unsigned num = seq.size();
 876                 for (unsigned i=0; i<num; i++) {
 877                         arg_diff = seq[i].diff(s);
 878                         // We apply the chain rule only when it makes sense.  This is not
 879                         // just for performance reasons but also to allow functions to
 880                         // throw when differentiated with respect to one of its arguments
 881                         // without running into trouble with our automatic full
 882                         // differentiation:
 883                         if (!arg_diff.is_zero())
 884                                 result += pderivative(i)*arg_diff;
 885                 }
 886         }
 887         return result;
 888 }
 889
 890 int function::compare_same_type(const basic & other) const
 891 {
 892         GINAC_ASSERT(is_of_type(other, function));
 893         const function & o = static_cast<const function &>(other);
 894
 895         if (serial != o.serial)
 896                 return serial < o.serial ? -1 : 1;
 897         else
 898                 return exprseq::compare_same_type(o);
 899 }
 900
 901 bool function::is_equal_same_type(const basic & other) const
 902 {
 903         GINAC_ASSERT(is_of_type(other, function));
 904         const function & o = static_cast<const function &>(other);
 905
 906         if (serial != o.serial)
 907                 return false;
 908         else
 909                 return exprseq::is_equal_same_type(o);
 910 }
 911
 912 bool function::match_same_type(const basic & other) const
 913 {
 914         GINAC_ASSERT(is_of_type(other, function));
 915         const function & o = static_cast<const function &>(other);
 916
 917         return serial == o.serial;
 918 }
 919
 920 unsigned function::return_type(void) const
 921 {
 922         const function_options &opt = registered_functions()[serial];
 923
 924         if (opt.use_return_type) {
 925                 // Return type was explicitly specified
 926                 return opt.return_type;
 927         } else {
 928                 // Default behavior is to use the return type of the first
 929                 // argument. Thus, exp() of a matrix behaves like a matrix, etc.
 930                 if (seq.empty())
 931                         return return_types::commutative;
 932                 else
 933                         return seq.begin()->return_type();
 934         }
 935 }
 936
 937 unsigned function::return_type_tinfo(void) const
 938 {
 939         const function_options &opt = registered_functions()[serial];
 940
 941         if (opt.use_return_type) {
 942                 // Return type was explicitly specified
 943                 return opt.return_type_tinfo;
 944         } else {
 945                 // Default behavior is to use the return type of the first
 946                 // argument. Thus, exp() of a matrix behaves like a matrix, etc.
 947                 if (seq.empty())
 948                         return tinfo_key;
 949                 else
 950                         return seq.begin()->return_type_tinfo();
 951         }
 952 }
 953
 954 //////////
 955 // new virtual functions which can be overridden by derived classes
 956 //////////
 957
 958 // none
 959
 960 //////////
 961 // non-virtual functions in this class
 962 //////////
 963
 964 // protected
 965
 966 ex function::pderivative(unsigned diff_param) const // partial differentiation
 967 {
 968         GINAC_ASSERT(serial<registered_functions().size());
 969
 970         // No derivative defined? Then return abstract derivative object
 971         if (registered_functions()[serial].derivative_f == NULL)
 972                 return fderivative(serial, diff_param, seq);
 973
 974         current_serial = serial;
 975         if (registered_functions()[serial].derivative_use_exvector_args)
 976                 return ((derivative_funcp_exvector)(registered_functions()[serial].derivative_f))(seq, diff_param);
 977         switch (registered_functions()[serial].nparams) {
 978                 // the following lines have been generated for max. ${maxargs} parameters
 979 ${diff_switch_statement}
 980                 // end of generated lines
 981         }
 982         throw(std::logic_error("function::pderivative(): no diff function defined"));
 983 }
 984
 985 std::vector<function_options> & function::registered_functions(void)
 986 {
 987         static std::vector<function_options> * rf = new std::vector<function_options>;
 988         return *rf;
 989 }
 990
 991 bool function::lookup_remember_table(ex & result) const
 992 {
 993         return remember_table::remember_tables()[serial].lookup_entry(*this,result);
 994 }
 995
 996 void function::store_remember_table(ex const & result) const
 997 {
 998         remember_table::remember_tables()[serial].add_entry(*this,result);
 999 }
1000
1001 // public
1002
1003 unsigned function::register_new(function_options const & opt)
1004 {
1005         unsigned same_name = 0;
1006         for (unsigned i=0; i<registered_functions().size(); ++i) {
1007                 if (registered_functions()[i].name==opt.name) {
1008                         ++same_name;
1009                 }
1010         }
1011         if (same_name>=opt.functions_with_same_name) {
1012                 // we do not throw an exception here because this code is
1013                 // usually executed before main(), so the exception could not
1014                 // caught anyhow
1015                 std::cerr << "WARNING: function name " << opt.name
1016                           << " already in use!" << std::endl;
1017         }
1018         registered_functions().push_back(opt);
1019         if (opt.use_remember) {
1020                 remember_table::remember_tables().
1021                         push_back(remember_table(opt.remember_size,
1022                                                  opt.remember_assoc_size,
1023                                                  opt.remember_strategy));
1024         } else {
1025                 remember_table::remember_tables().push_back(remember_table());
1026         }
1027         return registered_functions().size()-1;
1028 }
1029
1030 /** Find serial number of function by name and number of parameters.
1031  *  Throws exception if function was not found. */
1032 unsigned function::find_function(const std::string &name, unsigned nparams)
1033 {
1034         std::vector<function_options>::const_iterator i = function::registered_functions().begin(), end = function::registered_functions().end();
1035         unsigned serial = 0;
1036         while (i != end) {
1037                 if (i->get_name() == name && i->get_nparams() == nparams)
1038                         return serial;
1039                 ++i;
1040                 ++serial;
1041         }
1042         throw (std::runtime_error("no function '" + name + "' with " + ToString(nparams) + " parameters defined"));
1043 }
1044
1045 /** Return the print name of the function. */
1046 std::string function::get_name(void) const
1047 {
1048         GINAC_ASSERT(serial<registered_functions().size());
1049         return registered_functions()[serial].name;
1050 }
1051
1052 } // namespace GiNaC
1053
1054 END_OF_IMPLEMENTATION
1055
1056 print "Creating interface file function.h...";
1057 open OUT,">function.h" or die "cannot open function.h";
1058 print OUT $interface;
1059 close OUT;
1060 print "ok.\n";
1061
1062 print "Creating implementation file function.cpp...";
1063 open OUT,">function.cpp" or die "cannot open function.cpp";
1064 print OUT $implementation;
1065 close OUT;
1066 print "ok.\n";
1067
1068 print "done.\n";