ginac/function.pl

   1 #  This perl script automatically generates function.h and function.cpp
   2
   3 #  function.pl options: \$maxargs=${maxargs}
   4 #
   5 #  GiNaC Copyright (C) 1999-2007 Johannes Gutenberg University Mainz, Germany
   6 #
   7 #  This program is free software; you can redistribute it and/or modify
   8 #  it under the terms of the GNU General Public License as published by
   9 #  the Free Software Foundation; either version 2 of the License, or
  10 #  (at your option) any later version.
  11 #
  12 #  This program is distributed in the hope that it will be useful,
  13 #  but WITHOUT ANY WARRANTY; without even the implied warranty of
  14 #  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  15 #  GNU General Public License for more details.
  16 #
  17 #  You should have received a copy of the GNU General Public License
  18 #  along with this program; if not, write to the Free Software
  19 #  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
  20
  21 $maxargs=14;
  22
  23 sub generate_seq {
  24         my ($seq_template,$n)=@_;
  25         my ($res,$N);
  26
  27         $res='';
  28         for ($N=1; $N<=$n; $N++) {
  29                 $res .= eval('"' . $seq_template . '"');
  30                 if ($N!=$n) {
  31                         $res .= ', ';
  32                 }
  33         }
  34         return $res;
  35 }
  36
  37 sub generate_from_to {
  38         my ($template,$seq_template1,$seq_template2,$seq_template3,$from,$to)=@_;
  39         my ($res,$N,$SEQ);
  40
  41         $res='';
  42         for ($N=$from; $N<=$to; $N++) {
  43                 $SEQ1=generate_seq($seq_template1,$N);
  44                 $SEQ2=generate_seq($seq_template2,$N);
  45                 $SEQ3=generate_seq($seq_template3,$N);
  46                 $res .= eval('"' . $template . '"');
  47                 $SEQ1=''; # to avoid main::SEQ1 used only once warning
  48                 $SEQ2=''; # same as above
  49                 $SEQ3=''; # same as above
  50         }
  51         return $res;
  52 }
  53
  54 sub generate {
  55         my ($template,$seq_template1,$seq_template2,$seq_template3)=@_;
  56         return generate_from_to($template,$seq_template1,$seq_template2,$seq_template3,1,$maxargs);
  57 }
  58
  59 $declare_function_macro = generate(
  60         <<'END_OF_DECLARE_FUNCTION_MACRO','typename T${N}','const T${N} & p${N}','GiNaC::ex(p${N})');
  61 #define DECLARE_FUNCTION_${N}P(NAME) \\
  62 class NAME##_SERIAL { public: static unsigned serial; }; \\
  63 const unsigned NAME##_NPARAMS = ${N}; \\
  64 template<${SEQ1}> const GiNaC::function NAME(${SEQ2}) { \\
  65         return GiNaC::function(NAME##_SERIAL::serial, ${SEQ3}); \\
  66 }
  67
  68 END_OF_DECLARE_FUNCTION_MACRO
  69
  70 $typedef_eval_funcp=generate(
  71 'typedef ex (* eval_funcp_${N})(${SEQ1});'."\n",
  72 'const ex &','','');
  73
  74 $typedef_evalf_funcp=generate(
  75 'typedef ex (* evalf_funcp_${N})(${SEQ1});'."\n",
  76 'const ex &','','');
  77
  78 $typedef_conjugate_funcp=generate(
  79 'typedef ex (* conjugate_funcp_${N})(${SEQ1});'."\n",
  80 'const ex &','','');
  81
  82 $typedef_derivative_funcp=generate(
  83 'typedef ex (* derivative_funcp_${N})(${SEQ1}, unsigned);'."\n",
  84 'const ex &','','');
  85
  86 $typedef_series_funcp=generate(
  87 'typedef ex (* series_funcp_${N})(${SEQ1}, const relational &, int, unsigned);'."\n",
  88 'const ex &','','');
  89
  90 $typedef_print_funcp=generate(
  91 'typedef void (* print_funcp_${N})(${SEQ1}, const print_context &);'."\n",
  92 'const ex &','','');
  93
  94 $eval_func_interface=generate('    function_options & eval_func(eval_funcp_${N} e);'."\n",'','','');
  95
  96 $evalf_func_interface=generate('    function_options & evalf_func(evalf_funcp_${N} ef);'."\n",'','','');
  97
  98 $conjugate_func_interface=generate('    function_options & conjugate_func(conjugate_funcp_${N} d);'."\n",'','','');
  99
 100 $derivative_func_interface=generate('    function_options & derivative_func(derivative_funcp_${N} d);'."\n",'','','');
 101
 102 $series_func_interface=generate('    function_options & series_func(series_funcp_${N} s);'."\n",'','','');
 103
 104 $print_func_interface=generate(
 105         <<'END_OF_PRINT_FUNC_INTERFACE','','','');
 106     template <class Ctx> function_options & print_func(print_funcp_${N} p)
 107     {
 108         test_and_set_nparams(${N});
 109         set_print_func(Ctx::get_class_info_static().options.get_id(), print_funcp(p));
 110         return *this;
 111     }
 112 END_OF_PRINT_FUNC_INTERFACE
 113
 114 $constructors_interface=generate(
 115 '    function(unsigned ser, ${SEQ1});'."\n",
 116 'const ex & param${N}','','');
 117
 118 $constructors_implementation=generate(
 119         <<'END_OF_CONSTRUCTORS_IMPLEMENTATION','const ex & param${N}','param${N}','');
 120 function::function(unsigned ser, ${SEQ1})
 121         : exprseq(${SEQ2}), serial(ser)
 122 {
 123         tinfo_key = TINFO_function;
 124 }
 125 END_OF_CONSTRUCTORS_IMPLEMENTATION
 126
 127 $eval_switch_statement=generate(
 128         <<'END_OF_EVAL_SWITCH_STATEMENT','seq[${N}-1]','','');
 129         case ${N}:
 130                 eval_result = ((eval_funcp_${N})(opt.eval_f))(${SEQ1});
 131                 break;
 132 END_OF_EVAL_SWITCH_STATEMENT
 133
 134 $evalf_switch_statement=generate(
 135         <<'END_OF_EVALF_SWITCH_STATEMENT','eseq[${N}-1]','','');
 136         case ${N}:
 137                 return ((evalf_funcp_${N})(opt.evalf_f))(${SEQ1});
 138 END_OF_EVALF_SWITCH_STATEMENT
 139
 140 $conjugate_switch_statement=generate(
 141         <<'END_OF_DIFF_SWITCH_STATEMENT','seq[${N}-1]','','');
 142         case ${N}:
 143                 return ((conjugate_funcp_${N})(opt.conjugate_f))(${SEQ1});
 144 END_OF_DIFF_SWITCH_STATEMENT
 145
 146 $diff_switch_statement=generate(
 147         <<'END_OF_DIFF_SWITCH_STATEMENT','seq[${N}-1]','','');
 148         case ${N}:
 149                 return ((derivative_funcp_${N})(opt.derivative_f))(${SEQ1},diff_param);
 150 END_OF_DIFF_SWITCH_STATEMENT
 151
 152 $series_switch_statement=generate(
 153         <<'END_OF_SERIES_SWITCH_STATEMENT','seq[${N}-1]','','');
 154         case ${N}:
 155                 try {
 156                         res = ((series_funcp_${N})(opt.series_f))(${SEQ1},r,order,options);
 157                 } catch (do_taylor) {
 158                         res = basic::series(r, order, options);
 159                 }
 160                 return res;
 161 END_OF_SERIES_SWITCH_STATEMENT
 162
 163 $print_switch_statement=generate(
 164         <<'END_OF_PRINT_SWITCH_STATEMENT','seq[${N}-1]','','');
 165                 case ${N}:
 166                         ((print_funcp_${N})(pdt[id]))(${SEQ1}, c);
 167                         break;
 168 END_OF_PRINT_SWITCH_STATEMENT
 169
 170 $eval_func_implementation=generate(
 171         <<'END_OF_EVAL_FUNC_IMPLEMENTATION','','','');
 172 function_options & function_options::eval_func(eval_funcp_${N} e)
 173 {
 174         test_and_set_nparams(${N});
 175         eval_f = eval_funcp(e);
 176         return *this;
 177 }
 178 END_OF_EVAL_FUNC_IMPLEMENTATION
 179
 180 $evalf_func_implementation=generate(
 181         <<'END_OF_EVALF_FUNC_IMPLEMENTATION','','','');
 182 function_options & function_options::evalf_func(evalf_funcp_${N} ef)
 183 {
 184         test_and_set_nparams(${N});
 185         evalf_f = evalf_funcp(ef);
 186         return *this;
 187 }
 188 END_OF_EVALF_FUNC_IMPLEMENTATION
 189
 190 $conjugate_func_implementation=generate(
 191         <<'END_OF_CONJUGATE_FUNC_IMPLEMENTATION','','','');
 192 function_options & function_options::conjugate_func(conjugate_funcp_${N} c)
 193 {
 194         test_and_set_nparams(${N});
 195         conjugate_f = conjugate_funcp(c);
 196         return *this;
 197 }
 198 END_OF_CONJUGATE_FUNC_IMPLEMENTATION
 199
 200 $derivative_func_implementation=generate(
 201         <<'END_OF_DERIVATIVE_FUNC_IMPLEMENTATION','','','');
 202 function_options & function_options::derivative_func(derivative_funcp_${N} d)
 203 {
 204         test_and_set_nparams(${N});
 205         derivative_f = derivative_funcp(d);
 206         return *this;
 207 }
 208 END_OF_DERIVATIVE_FUNC_IMPLEMENTATION
 209
 210 $series_func_implementation=generate(
 211         <<'END_OF_SERIES_FUNC_IMPLEMENTATION','','','');
 212 function_options & function_options::series_func(series_funcp_${N} s)
 213 {
 214         test_and_set_nparams(${N});
 215         series_f = series_funcp(s);
 216         return *this;
 217 }
 218 END_OF_SERIES_FUNC_IMPLEMENTATION
 219
 220 $interface=<<END_OF_INTERFACE;
 221 /** \@file function.h
 222  *
 223  *  Interface to class of symbolic functions. */
 224
 225 /*
 226  *  This file was generated automatically by function.pl.
 227  *  Please do not modify it directly, edit the perl script instead!
 228  *  function.pl options: \$maxargs=${maxargs}
 229  *
 230  *  GiNaC Copyright (C) 1999-2007 Johannes Gutenberg University Mainz, Germany
 231  *
 232  *  This program is free software; you can redistribute it and/or modify
 233  *  it under the terms of the GNU General Public License as published by
 234  *  the Free Software Foundation; either version 2 of the License, or
 235  *  (at your option) any later version.
 236  *
 237  *  This program is distributed in the hope that it will be useful,
 238  *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 239  *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 240  *  GNU General Public License for more details.
 241  *
 242  *  You should have received a copy of the GNU General Public License
 243  *  along with this program; if not, write to the Free Software
 244  *  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
 245  */
 246
 247 #ifndef __GINAC_FUNCTION_H__
 248 #define __GINAC_FUNCTION_H__
 249
 250 #include <string>
 251 #include <vector>
 252
 253 // CINT needs <algorithm> to work properly with <vector>
 254 #include <algorithm>
 255
 256 #include "exprseq.h"
 257
 258 // the following lines have been generated for max. ${maxargs} parameters
 259 $declare_function_macro
 260 // end of generated lines
 261
 262 #define REGISTER_FUNCTION(NAME,OPT) \\
 263 unsigned NAME##_SERIAL::serial = \\
 264         GiNaC::function::register_new(GiNaC::function_options(#NAME, NAME##_NPARAMS).OPT);
 265
 266 namespace GiNaC {
 267
 268 class function;
 269 class symmetry;
 270
 271 typedef ex (* eval_funcp)();
 272 typedef ex (* evalf_funcp)();
 273 typedef ex (* conjugate_funcp)();
 274 typedef ex (* derivative_funcp)();
 275 typedef ex (* series_funcp)();
 276 typedef void (* print_funcp)();
 277
 278 // the following lines have been generated for max. ${maxargs} parameters
 279 $typedef_eval_funcp
 280 $typedef_evalf_funcp
 281 $typedef_conjugate_funcp
 282 $typedef_derivative_funcp
 283 $typedef_series_funcp
 284 $typedef_print_funcp
 285 // end of generated lines
 286
 287 // Alternatively, an exvector may be passed into the static function, instead
 288 // of individual ex objects.  Then, the number of arguments is not limited.
 289 typedef ex (* eval_funcp_exvector)(const exvector &);
 290 typedef ex (* evalf_funcp_exvector)(const exvector &);
 291 typedef ex (* conjugate_funcp_exvector)(const exvector &);
 292 typedef ex (* derivative_funcp_exvector)(const exvector &, unsigned);
 293 typedef ex (* series_funcp_exvector)(const exvector &, const relational &, int, unsigned);
 294 typedef void (* print_funcp_exvector)(const exvector &, const print_context &);
 295
 296
 297 class function_options
 298 {
 299         friend class function;
 300         friend class fderivative;
 301 public:
 302         function_options();
 303         function_options(std::string const & n, std::string const & tn=std::string());
 304         function_options(std::string const & n, unsigned np);
 305         ~function_options();
 306         void initialize();
 307
 308         function_options & dummy() { return *this; }
 309         function_options & set_name(std::string const & n, std::string const & tn=std::string());
 310         function_options & latex_name(std::string const & tn);
 311 // the following lines have been generated for max. ${maxargs} parameters
 312 $eval_func_interface
 313 $evalf_func_interface
 314 $conjugate_func_interface
 315 $derivative_func_interface
 316 $series_func_interface
 317 $print_func_interface
 318 // end of generated lines
 319         function_options & eval_func(eval_funcp_exvector e);
 320         function_options & evalf_func(evalf_funcp_exvector ef);
 321         function_options & conjugate_func(conjugate_funcp_exvector d);
 322         function_options & derivative_func(derivative_funcp_exvector d);
 323         function_options & series_func(series_funcp_exvector s);
 324
 325         template <class Ctx> function_options & print_func(print_funcp_exvector p)
 326         {
 327                 print_use_exvector_args = true;
 328                 set_print_func(Ctx::get_class_info_static().options.get_id(), print_funcp(p));
 329                 return *this;
 330         }
 331
 332         function_options & set_return_type(unsigned rt, unsigned rtt=0);
 333         function_options & do_not_evalf_params();
 334         function_options & remember(unsigned size, unsigned assoc_size=0,
 335                                     unsigned strategy=remember_strategies::delete_never);
 336         function_options & overloaded(unsigned o);
 337         function_options & set_symmetry(const symmetry & s);
 338
 339         std::string get_name() const { return name; }
 340         unsigned get_nparams() const { return nparams; }
 341
 342 protected:
 343         bool has_derivative() const { return derivative_f != NULL; }
 344         void test_and_set_nparams(unsigned n);
 345         void set_print_func(unsigned id, print_funcp f);
 346
 347         std::string name;
 348         std::string TeX_name;
 349
 350         unsigned nparams;
 351
 352         eval_funcp eval_f;
 353         evalf_funcp evalf_f;
 354         conjugate_funcp conjugate_f;
 355         derivative_funcp derivative_f;
 356         series_funcp series_f;
 357         std::vector<print_funcp> print_dispatch_table;
 358
 359         bool evalf_params_first;
 360
 361         bool use_return_type;
 362         unsigned return_type;
 363         unsigned return_type_tinfo;
 364
 365         bool use_remember;
 366         unsigned remember_size;
 367         unsigned remember_assoc_size;
 368         unsigned remember_strategy;
 369
 370         bool eval_use_exvector_args;
 371         bool evalf_use_exvector_args;
 372         bool conjugate_use_exvector_args;
 373         bool derivative_use_exvector_args;
 374         bool series_use_exvector_args;
 375         bool print_use_exvector_args;
 376
 377         unsigned functions_with_same_name;
 378
 379         ex symtree;
 380 };
 381
 382
 383 /** Exception class thrown by classes which provide their own series expansion
 384  *  to signal that ordinary Taylor expansion is safe. */
 385 class do_taylor {};
 386
 387
 388 /** The class function is used to implement builtin functions like sin, cos...
 389         and user defined functions */
 390 class function : public exprseq
 391 {
 392         GINAC_DECLARE_REGISTERED_CLASS(function, exprseq)
 393
 394         // CINT has a linking problem
 395 #ifndef __MAKECINT__
 396         friend void ginsh_get_ginac_functions();
 397 #endif // def __MAKECINT__
 398
 399         friend class remember_table_entry;
 400         // friend class remember_table_list;
 401         // friend class remember_table;
 402
 403 // member functions
 404
 405         // other constructors
 406 public:
 407         function(unsigned ser);
 408         // the following lines have been generated for max. ${maxargs} parameters
 409 $constructors_interface
 410         // end of generated lines
 411         function(unsigned ser, const exprseq & es);
 412         function(unsigned ser, const exvector & v, bool discardable = false);
 413         function(unsigned ser, std::auto_ptr<exvector> vp);
 414
 415         // functions overriding virtual functions from base classes
 416 public:
 417         void print(const print_context & c, unsigned level = 0) const;
 418         unsigned precedence() const {return 70;}
 419         ex expand(unsigned options=0) const;
 420         ex eval(int level=0) const;
 421         ex evalf(int level=0) const;
 422         unsigned calchash() const;
 423         ex series(const relational & r, int order, unsigned options = 0) const;
 424         ex thiscontainer(const exvector & v) const;
 425         ex thiscontainer(std::auto_ptr<exvector> vp) const;
 426         ex conjugate() const;
 427 protected:
 428         ex derivative(const symbol & s) const;
 429         bool is_equal_same_type(const basic & other) const;
 430         bool match_same_type(const basic & other) const;
 431         unsigned return_type() const;
 432         unsigned return_type_tinfo() const;
 433
 434         // new virtual functions which can be overridden by derived classes
 435         // none
 436
 437         // non-virtual functions in this class
 438 protected:
 439         ex pderivative(unsigned diff_param) const; // partial differentiation
 440         static std::vector<function_options> & registered_functions();
 441         bool lookup_remember_table(ex & result) const;
 442         void store_remember_table(ex const & result) const;
 443 public:
 444         static unsigned register_new(function_options const & opt);
 445         static unsigned current_serial;
 446         static unsigned find_function(const std::string &name, unsigned nparams);
 447         unsigned get_serial() const {return serial;}
 448         std::string get_name() const;
 449
 450 // member variables
 451
 452 protected:
 453         unsigned serial;
 454 };
 455
 456 // utility functions/macros
 457
 458 /** Specialization of is_exactly_a<function>(obj) for objects of type function. */
 459 template<> inline bool is_exactly_a<function>(const basic & obj)
 460 {
 461         return obj.tinfo()==TINFO_function;
 462 }
 463
 464 template <typename T>
 465 inline bool is_the_function(const ex & x)
 466 {
 467         return is_exactly_a<function>(x)
 468             && ex_to<function>(x).get_serial() == T::serial;
 469 }
 470
 471 // Check whether OBJ is the specified symbolic function.
 472 #define is_ex_the_function(OBJ, FUNCNAME) (GiNaC::is_the_function<FUNCNAME##_SERIAL>(OBJ))
 473
 474 } // namespace GiNaC
 475
 476 #endif // ndef __GINAC_FUNCTION_H__
 477
 478 END_OF_INTERFACE
 479
 480 $implementation=<<END_OF_IMPLEMENTATION;
 481 /** \@file function.cpp
 482  *
 483  *  Implementation of class of symbolic functions. */
 484
 485 /*
 486  *  This file was generated automatically by function.pl.
 487  *  Please do not modify it directly, edit the perl script instead!
 488  *  function.pl options: \$maxargs=${maxargs}
 489  *
 490  *  GiNaC Copyright (C) 1999-2007 Johannes Gutenberg University Mainz, Germany
 491  *
 492  *  This program is free software; you can redistribute it and/or modify
 493  *  it under the terms of the GNU General Public License as published by
 494  *  the Free Software Foundation; either version 2 of the License, or
 495  *  (at your option) any later version.
 496  *
 497  *  This program is distributed in the hope that it will be useful,
 498  *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 499  *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 500  *  GNU General Public License for more details.
 501  *
 502  *  You should have received a copy of the GNU General Public License
 503  *  along with this program; if not, write to the Free Software
 504  *  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
 505  */
 506
 507 #include <iostream>
 508 #include <string>
 509 #include <stdexcept>
 510 #include <list>
 511 #include <limits>
 512
 513 #include "function.h"
 514 #include "operators.h"
 515 #include "fderivative.h"
 516 #include "ex.h"
 517 #include "lst.h"
 518 #include "symmetry.h"
 519 #include "print.h"
 520 #include "archive.h"
 521 #include "inifcns.h"
 522 #include "tostring.h"
 523 #include "utils.h"
 524 #include "remember.h"
 525
 526 namespace GiNaC {
 527
 528 //////////
 529 // helper class function_options
 530 //////////
 531
 532 function_options::function_options()
 533 {
 534         initialize();
 535 }
 536
 537 function_options::function_options(std::string const & n, std::string const & tn)
 538 {
 539         initialize();
 540         set_name(n, tn);
 541 }
 542
 543 function_options::function_options(std::string const & n, unsigned np)
 544 {
 545         initialize();
 546         set_name(n, std::string());
 547         nparams = np;
 548 }
 549
 550 function_options::~function_options()
 551 {
 552         // nothing to clean up at the moment
 553 }
 554
 555 void function_options::initialize()
 556 {
 557         set_name("unnamed_function", "\\\\mbox{unnamed}");
 558         nparams = 0;
 559         eval_f = evalf_f = conjugate_f = derivative_f = series_f = 0;
 560         evalf_params_first = true;
 561         use_return_type = false;
 562         eval_use_exvector_args = false;
 563         evalf_use_exvector_args = false;
 564         conjugate_use_exvector_args = false;
 565         derivative_use_exvector_args = false;
 566         series_use_exvector_args = false;
 567         print_use_exvector_args = false;
 568         use_remember = false;
 569         functions_with_same_name = 1;
 570         symtree = 0;
 571 }
 572
 573 function_options & function_options::set_name(std::string const & n,
 574                                               std::string const & tn)
 575 {
 576         name = n;
 577         if (tn==std::string())
 578                 TeX_name = "\\\\mbox{"+name+"}";
 579         else
 580                 TeX_name = tn;
 581         return *this;
 582 }
 583
 584 function_options & function_options::latex_name(std::string const & tn)
 585 {
 586         TeX_name = tn;
 587         return *this;
 588 }
 589
 590 // the following lines have been generated for max. ${maxargs} parameters
 591 $eval_func_implementation
 592 $evalf_func_implementation
 593 $conjugate_func_implementation
 594 $derivative_func_implementation
 595 $series_func_implementation
 596 // end of generated lines
 597
 598 function_options& function_options::eval_func(eval_funcp_exvector e)
 599 {
 600         eval_use_exvector_args = true;
 601         eval_f = eval_funcp(e);
 602         return *this;
 603 }
 604 function_options& function_options::evalf_func(evalf_funcp_exvector ef)
 605 {
 606         evalf_use_exvector_args = true;
 607         evalf_f = evalf_funcp(ef);
 608         return *this;
 609 }
 610 function_options& function_options::conjugate_func(conjugate_funcp_exvector c)
 611 {
 612         conjugate_use_exvector_args = true;
 613         conjugate_f = conjugate_funcp(c);
 614         return *this;
 615 }
 616 function_options& function_options::derivative_func(derivative_funcp_exvector d)
 617 {
 618         derivative_use_exvector_args = true;
 619         derivative_f = derivative_funcp(d);
 620         return *this;
 621 }
 622 function_options& function_options::series_func(series_funcp_exvector s)
 623 {
 624         series_use_exvector_args = true;
 625         series_f = series_funcp(s);
 626         return *this;
 627 }
 628
 629 function_options & function_options::set_return_type(unsigned rt, unsigned rtt)
 630 {
 631         use_return_type = true;
 632         return_type = rt;
 633         return_type_tinfo = rtt;
 634         return *this;
 635 }
 636
 637 function_options & function_options::do_not_evalf_params()
 638 {
 639         evalf_params_first = false;
 640         return *this;
 641 }
 642
 643 function_options & function_options::remember(unsigned size,
 644                                               unsigned assoc_size,
 645                                               unsigned strategy)
 646 {
 647         use_remember = true;
 648         remember_size = size;
 649         remember_assoc_size = assoc_size;
 650         remember_strategy = strategy;
 651         return *this;
 652 }
 653
 654 function_options & function_options::overloaded(unsigned o)
 655 {
 656         functions_with_same_name = o;
 657         return *this;
 658 }
 659
 660 function_options & function_options::set_symmetry(const symmetry & s)
 661 {
 662         symtree = s;
 663         return *this;
 664 }
 665
 666 void function_options::test_and_set_nparams(unsigned n)
 667 {
 668         if (nparams==0) {
 669                 nparams = n;
 670         } else if (nparams!=n) {
 671                 // we do not throw an exception here because this code is
 672                 // usually executed before main(), so the exception could not
 673                 // be caught anyhow
 674                 std::cerr << "WARNING: " << name << "(): number of parameters ("
 675                           << n << ") differs from number set before ("
 676                           << nparams << ")" << std::endl;
 677         }
 678 }
 679
 680 void function_options::set_print_func(unsigned id, print_funcp f)
 681 {
 682         if (id >= print_dispatch_table.size())
 683                 print_dispatch_table.resize(id + 1);
 684         print_dispatch_table[id] = f;
 685 }
 686
 687 /** This can be used as a hook for external applications. */
 688 unsigned function::current_serial = 0;
 689
 690
 691 GINAC_IMPLEMENT_REGISTERED_CLASS(function, exprseq)
 692
 693 //////////
 694 // default constructor
 695 //////////
 696
 697 // public
 698
 699 function::function() : serial(0)
 700 {
 701         tinfo_key = TINFO_function;
 702 }
 703
 704 //////////
 705 // other constructors
 706 //////////
 707
 708 // public
 709
 710 function::function(unsigned ser) : serial(ser)
 711 {
 712         tinfo_key = TINFO_function;
 713 }
 714
 715 // the following lines have been generated for max. ${maxargs} parameters
 716 $constructors_implementation
 717 // end of generated lines
 718
 719 function::function(unsigned ser, const exprseq & es) : exprseq(es), serial(ser)
 720 {
 721         tinfo_key = TINFO_function;
 722
 723         // Force re-evaluation even if the exprseq was already evaluated
 724         // (the exprseq copy constructor copies the flags)
 725         clearflag(status_flags::evaluated);
 726 }
 727
 728 function::function(unsigned ser, const exvector & v, bool discardable)
 729   : exprseq(v,discardable), serial(ser)
 730 {
 731         tinfo_key = TINFO_function;
 732 }
 733
 734 function::function(unsigned ser, std::auto_ptr<exvector> vp)
 735   : exprseq(vp), serial(ser)
 736 {
 737         tinfo_key = TINFO_function;
 738 }
 739
 740 //////////
 741 // archiving
 742 //////////
 743
 744 /** Construct object from archive_node. */
 745 function::function(const archive_node &n, lst &sym_lst) : inherited(n, sym_lst)
 746 {
 747         // Find serial number by function name
 748         std::string s;
 749         if (n.find_string("name", s)) {
 750                 unsigned int ser = 0;
 751                 std::vector<function_options>::const_iterator i = registered_functions().begin(), iend = registered_functions().end();
 752                 while (i != iend) {
 753                         if (s == i->name) {
 754                                 serial = ser;
 755                                 return;
 756                         }
 757                         ++i; ++ser;
 758                 }
 759                 throw (std::runtime_error("unknown function '" + s + "' in archive"));
 760         } else
 761                 throw (std::runtime_error("unnamed function in archive"));
 762 }
 763
 764 /** Unarchive the object. */
 765 ex function::unarchive(const archive_node &n, lst &sym_lst)
 766 {
 767         return (new function(n, sym_lst))->setflag(status_flags::dynallocated);
 768 }
 769
 770 /** Archive the object. */
 771 void function::archive(archive_node &n) const
 772 {
 773         inherited::archive(n);
 774         GINAC_ASSERT(serial < registered_functions().size());
 775         n.add_string("name", registered_functions()[serial].name);
 776 }
 777
 778 //////////
 779 // functions overriding virtual functions from base classes
 780 //////////
 781
 782 // public
 783
 784 void function::print(const print_context & c, unsigned level) const
 785 {
 786         GINAC_ASSERT(serial<registered_functions().size());
 787         const function_options &opt = registered_functions()[serial];
 788         const std::vector<print_funcp> &pdt = opt.print_dispatch_table;
 789
 790         // Dynamically dispatch on print_context type
 791         const print_context_class_info *pc_info = &c.get_class_info();
 792
 793 next_context:
 794         unsigned id = pc_info->options.get_id();
 795         if (id >= pdt.size() || pdt[id] == NULL) {
 796
 797                 // Method not found, try parent print_context class
 798                 const print_context_class_info *parent_pc_info = pc_info->get_parent();
 799                 if (parent_pc_info) {
 800                         pc_info = parent_pc_info;
 801                         goto next_context;
 802                 }
 803
 804                 // Method still not found, use default output
 805                 if (is_a<print_tree>(c)) {
 806
 807                         c.s << std::string(level, ' ') << class_name() << " "
 808                             << opt.name << " @" << this
 809                             << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
 810                             << ", nops=" << nops()
 811                             << std::endl;
 812                         unsigned delta_indent = static_cast<const print_tree &>(c).delta_indent;
 813                         for (size_t i=0; i<seq.size(); ++i)
 814                                 seq[i].print(c, level + delta_indent);
 815                         c.s << std::string(level + delta_indent, ' ') << "=====" << std::endl;
 816
 817                 } else if (is_a<print_csrc>(c)) {
 818
 819                         // Print function name in lowercase
 820                         std::string lname = opt.name;
 821                         size_t num = lname.size();
 822                         for (size_t i=0; i<num; i++)
 823                                 lname[i] = tolower(lname[i]);
 824                         c.s << lname;
 825                         printseq(c, '(', ',', ')', exprseq::precedence(), function::precedence());
 826
 827                 } else if (is_a<print_latex>(c)) {
 828                         c.s << opt.TeX_name;
 829                         printseq(c, '(', ',', ')', exprseq::precedence(), function::precedence());
 830                 } else {
 831                         c.s << opt.name;
 832                         printseq(c, '(', ',', ')', exprseq::precedence(), function::precedence());
 833                 }
 834
 835         } else {
 836
 837                 // Method found, call it
 838                 current_serial = serial;
 839                 if (opt.print_use_exvector_args)
 840                         ((print_funcp_exvector)pdt[id])(seq, c);
 841                 else switch (opt.nparams) {
 842                         // the following lines have been generated for max. ${maxargs} parameters
 843 ${print_switch_statement}
 844                         // end of generated lines
 845                 default:
 846                         throw(std::logic_error("function::print(): invalid nparams"));
 847                 }
 848         }
 849 }
 850
 851 ex function::expand(unsigned options) const
 852 {
 853         // Only expand arguments when asked to do so
 854         if (options & expand_options::expand_function_args)
 855                 return inherited::expand(options);
 856         else
 857                 return (options == 0) ? setflag(status_flags::expanded) : *this;
 858 }
 859
 860 ex function::eval(int level) const
 861 {
 862         if (level>1) {
 863                 // first evaluate children, then we will end up here again
 864                 return function(serial,evalchildren(level));
 865         }
 866
 867         GINAC_ASSERT(serial<registered_functions().size());
 868         const function_options &opt = registered_functions()[serial];
 869
 870         // Canonicalize argument order according to the symmetry properties
 871         if (seq.size() > 1 && !(opt.symtree.is_zero())) {
 872                 exvector v = seq;
 873                 GINAC_ASSERT(is_a<symmetry>(opt.symtree));
 874                 int sig = canonicalize(v.begin(), ex_to<symmetry>(opt.symtree));
 875                 if (sig != std::numeric_limits<int>::max()) {
 876                         // Something has changed while sorting arguments, more evaluations later
 877                         if (sig == 0)
 878                                 return _ex0;
 879                         return ex(sig) * thiscontainer(v);
 880                 }
 881         }
 882
 883         if (opt.eval_f==0) {
 884                 return this->hold();
 885         }
 886
 887         bool use_remember = opt.use_remember;
 888         ex eval_result;
 889         if (use_remember && lookup_remember_table(eval_result)) {
 890                 return eval_result;
 891         }
 892         current_serial = serial;
 893         if (opt.eval_use_exvector_args)
 894                 eval_result = ((eval_funcp_exvector)(opt.eval_f))(seq);
 895         else
 896         switch (opt.nparams) {
 897                 // the following lines have been generated for max. ${maxargs} parameters
 898 ${eval_switch_statement}
 899                 // end of generated lines
 900         default:
 901                 throw(std::logic_error("function::eval(): invalid nparams"));
 902         }
 903         if (use_remember) {
 904                 store_remember_table(eval_result);
 905         }
 906         return eval_result;
 907 }
 908
 909 ex function::evalf(int level) const
 910 {
 911         GINAC_ASSERT(serial<registered_functions().size());
 912         const function_options &opt = registered_functions()[serial];
 913
 914         // Evaluate children first
 915         exvector eseq;
 916         if (level == 1 || !(opt.evalf_params_first))
 917                 eseq = seq;
 918         else if (level == -max_recursion_level)
 919                 throw(std::runtime_error("max recursion level reached"));
 920         else {
 921                 eseq.reserve(seq.size());
 922                 --level;
 923                 exvector::const_iterator it = seq.begin(), itend = seq.end();
 924                 while (it != itend) {
 925                         eseq.push_back(it->evalf(level));
 926                         ++it;
 927                 }
 928         }
 929
 930         if (opt.evalf_f==0) {
 931                 return function(serial,eseq).hold();
 932         }
 933         current_serial = serial;
 934         if (opt.evalf_use_exvector_args)
 935                 return ((evalf_funcp_exvector)(opt.evalf_f))(seq);
 936         switch (opt.nparams) {
 937                 // the following lines have been generated for max. ${maxargs} parameters
 938 ${evalf_switch_statement}
 939                 // end of generated lines
 940         }
 941         throw(std::logic_error("function::evalf(): invalid nparams"));
 942 }
 943
 944 unsigned function::calchash() const
 945 {
 946         unsigned v = golden_ratio_hash(golden_ratio_hash(tinfo()) ^ serial);
 947         for (size_t i=0; i<nops(); i++) {
 948                 v = rotate_left(v);
 949                 v ^= this->op(i).gethash();
 950         }
 951
 952         if (flags & status_flags::evaluated) {
 953                 setflag(status_flags::hash_calculated);
 954                 hashvalue = v;
 955         }
 956         return v;
 957 }
 958
 959 ex function::thiscontainer(const exvector & v) const
 960 {
 961         return function(serial, v);
 962 }
 963
 964 ex function::thiscontainer(std::auto_ptr<exvector> vp) const
 965 {
 966         return function(serial, vp);
 967 }
 968
 969 /** Implementation of ex::series for functions.
 970  *  \@see ex::series */
 971 ex function::series(const relational & r, int order, unsigned options) const
 972 {
 973         GINAC_ASSERT(serial<registered_functions().size());
 974         const function_options &opt = registered_functions()[serial];
 975
 976         if (opt.series_f==0) {
 977                 return basic::series(r, order);
 978         }
 979         ex res;
 980         current_serial = serial;
 981         if (opt.series_use_exvector_args) {
 982                 try {
 983                         res = ((series_funcp_exvector)(opt.series_f))(seq, r, order, options);
 984                 } catch (do_taylor) {
 985                         res = basic::series(r, order, options);
 986                 }
 987                 return res;
 988         }
 989         switch (opt.nparams) {
 990                 // the following lines have been generated for max. ${maxargs} parameters
 991 ${series_switch_statement}
 992                 // end of generated lines
 993         }
 994         throw(std::logic_error("function::series(): invalid nparams"));
 995 }
 996
 997 /** Implementation of ex::conjugate for functions. */
 998 ex function::conjugate() const
 999 {
1000         GINAC_ASSERT(serial<registered_functions().size());
1001         const function_options & opt = registered_functions()[serial];
1002
1003         if (opt.conjugate_f==0) {
1004                 return exprseq::conjugate();
1005         }
1006
1007         if (opt.conjugate_use_exvector_args) {
1008                 return ((conjugate_funcp_exvector)(opt.conjugate_f))(seq);
1009         }
1010
1011         switch (opt.nparams) {
1012                 // the following lines have been generated for max. ${maxargs} parameters
1013 ${conjugate_switch_statement}
1014                 // end of generated lines
1015         }
1016         throw(std::logic_error("function::conjugate(): invalid nparams"));
1017 }
1018
1019 // protected
1020
1021 /** Implementation of ex::diff() for functions. It applies the chain rule,
1022  *  except for the Order term function.
1023  *  \@see ex::diff */
1024 ex function::derivative(const symbol & s) const
1025 {
1026         ex result;
1027
1028         if (serial == Order_SERIAL::serial) {
1029                 // Order Term function only differentiates the argument
1030                 return Order(seq[0].diff(s));
1031         } else {
1032                 // Chain rule
1033                 ex arg_diff;
1034                 size_t num = seq.size();
1035                 for (size_t i=0; i<num; i++) {
1036                         arg_diff = seq[i].diff(s);
1037                         // We apply the chain rule only when it makes sense.  This is not
1038                         // just for performance reasons but also to allow functions to
1039                         // throw when differentiated with respect to one of its arguments
1040                         // without running into trouble with our automatic full
1041                         // differentiation:
1042                         if (!arg_diff.is_zero())
1043                                 result += pderivative(i)*arg_diff;
1044                 }
1045         }
1046         return result;
1047 }
1048
1049 int function::compare_same_type(const basic & other) const
1050 {
1051         GINAC_ASSERT(is_a<function>(other));
1052         const function & o = static_cast<const function &>(other);
1053
1054         if (serial != o.serial)
1055                 return serial < o.serial ? -1 : 1;
1056         else
1057                 return exprseq::compare_same_type(o);
1058 }
1059
1060 bool function::is_equal_same_type(const basic & other) const
1061 {
1062         GINAC_ASSERT(is_a<function>(other));
1063         const function & o = static_cast<const function &>(other);
1064
1065         if (serial != o.serial)
1066                 return false;
1067         else
1068                 return exprseq::is_equal_same_type(o);
1069 }
1070
1071 bool function::match_same_type(const basic & other) const
1072 {
1073         GINAC_ASSERT(is_a<function>(other));
1074         const function & o = static_cast<const function &>(other);
1075
1076         return serial == o.serial;
1077 }
1078
1079 unsigned function::return_type() const
1080 {
1081         GINAC_ASSERT(serial<registered_functions().size());
1082         const function_options &opt = registered_functions()[serial];
1083
1084         if (opt.use_return_type) {
1085                 // Return type was explicitly specified
1086                 return opt.return_type;
1087         } else {
1088                 // Default behavior is to use the return type of the first
1089                 // argument. Thus, exp() of a matrix behaves like a matrix, etc.
1090                 if (seq.empty())
1091                         return return_types::commutative;
1092                 else
1093                         return seq.begin()->return_type();
1094         }
1095 }
1096
1097 unsigned function::return_type_tinfo() const
1098 {
1099         GINAC_ASSERT(serial<registered_functions().size());
1100         const function_options &opt = registered_functions()[serial];
1101
1102         if (opt.use_return_type) {
1103                 // Return type was explicitly specified
1104                 return opt.return_type_tinfo;
1105         } else {
1106                 // Default behavior is to use the return type of the first
1107                 // argument. Thus, exp() of a matrix behaves like a matrix, etc.
1108                 if (seq.empty())
1109                         return tinfo_key;
1110                 else
1111                         return seq.begin()->return_type_tinfo();
1112         }
1113 }
1114
1115 //////////
1116 // new virtual functions which can be overridden by derived classes
1117 //////////
1118
1119 // none
1120
1121 //////////
1122 // non-virtual functions in this class
1123 //////////
1124
1125 // protected
1126
1127 ex function::pderivative(unsigned diff_param) const // partial differentiation
1128 {
1129         GINAC_ASSERT(serial<registered_functions().size());
1130         const function_options &opt = registered_functions()[serial];
1131
1132         // No derivative defined? Then return abstract derivative object
1133         if (opt.derivative_f == NULL)
1134                 return fderivative(serial, diff_param, seq);
1135
1136         current_serial = serial;
1137         if (opt.derivative_use_exvector_args)
1138                 return ((derivative_funcp_exvector)(opt.derivative_f))(seq, diff_param);
1139         switch (opt.nparams) {
1140                 // the following lines have been generated for max. ${maxargs} parameters
1141 ${diff_switch_statement}
1142                 // end of generated lines
1143         }
1144         throw(std::logic_error("function::pderivative(): no diff function defined"));
1145 }
1146
1147 std::vector<function_options> & function::registered_functions()
1148 {
1149         static std::vector<function_options> * rf = new std::vector<function_options>;
1150         return *rf;
1151 }
1152
1153 bool function::lookup_remember_table(ex & result) const
1154 {
1155         return remember_table::remember_tables()[this->serial].lookup_entry(*this,result);
1156 }
1157
1158 void function::store_remember_table(ex const & result) const
1159 {
1160         remember_table::remember_tables()[this->serial].add_entry(*this,result);
1161 }
1162
1163 // public
1164
1165 unsigned function::register_new(function_options const & opt)
1166 {
1167         size_t same_name = 0;
1168         for (size_t i=0; i<registered_functions().size(); ++i) {
1169                 if (registered_functions()[i].name==opt.name) {
1170                         ++same_name;
1171                 }
1172         }
1173         if (same_name>=opt.functions_with_same_name) {
1174                 // we do not throw an exception here because this code is
1175                 // usually executed before main(), so the exception could not
1176                 // caught anyhow
1177                 std::cerr << "WARNING: function name " << opt.name
1178                           << " already in use!" << std::endl;
1179         }
1180         registered_functions().push_back(opt);
1181         if (opt.use_remember) {
1182                 remember_table::remember_tables().
1183                         push_back(remember_table(opt.remember_size,
1184                                                  opt.remember_assoc_size,
1185                                                  opt.remember_strategy));
1186         } else {
1187                 remember_table::remember_tables().push_back(remember_table());
1188         }
1189         return registered_functions().size()-1;
1190 }
1191
1192 /** Find serial number of function by name and number of parameters.
1193  *  Throws exception if function was not found. */
1194 unsigned function::find_function(const std::string &name, unsigned nparams)
1195 {
1196         std::vector<function_options>::const_iterator i = function::registered_functions().begin(), end = function::registered_functions().end();
1197         unsigned serial = 0;
1198         while (i != end) {
1199                 if (i->get_name() == name && i->get_nparams() == nparams)
1200                         return serial;
1201                 ++i;
1202                 ++serial;
1203         }
1204         throw (std::runtime_error("no function '" + name + "' with " + ToString(nparams) + " parameters defined"));
1205 }
1206
1207 /** Return the print name of the function. */
1208 std::string function::get_name() const
1209 {
1210         GINAC_ASSERT(serial<registered_functions().size());
1211         return registered_functions()[serial].name;
1212 }
1213
1214 } // namespace GiNaC
1215
1216 END_OF_IMPLEMENTATION
1217
1218 print "Creating interface file function.h...";
1219 open OUT,">function.h" or die "cannot open function.h";
1220 print OUT $interface;
1221 close OUT;
1222 print "ok.\n";
1223
1224 print "Creating implementation file function.cpp...";
1225 open OUT,">function.cpp" or die "cannot open function.cpp";
1226 print OUT $implementation;
1227 close OUT;
1228 print "ok.\n";
1229
1230 print "done.\n";