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 class NAME##_SERIAL { public: static unsigned serial; }; \\
  43 template<${SEQ1}> const GiNaC::function NAME(${SEQ2}) { \\
  44         return GiNaC::function(NAME##_SERIAL::serial, ${SEQ3}); \\
  45 }
  46
  47 END_OF_DECLARE_FUNCTION_MACRO
  48
  49 $typedef_eval_funcp=generate(
  50 'typedef ex (* eval_funcp_${N})(${SEQ1});'."\n",
  51 'const ex &','','');
  52
  53 $typedef_evalf_funcp=generate(
  54 'typedef ex (* evalf_funcp_${N})(${SEQ1});'."\n",
  55 'const ex &','','');
  56
  57 $typedef_derivative_funcp=generate(
  58 'typedef ex (* derivative_funcp_${N})(${SEQ1}, unsigned);'."\n",
  59 'const ex &','','');
  60
  61 $typedef_series_funcp=generate(
  62 'typedef ex (* series_funcp_${N})(${SEQ1}, const relational &, int, unsigned);'."\n",
  63 'const ex &','','');
  64
  65 $typedef_print_funcp=generate(
  66 'typedef void (* print_funcp_${N})(${SEQ1}, const print_context &);'."\n",
  67 'const ex &','','');
  68
  69 $eval_func_interface=generate('    function_options & eval_func(eval_funcp_${N} e);'."\n",'','','');
  70
  71 $evalf_func_interface=generate('    function_options & evalf_func(evalf_funcp_${N} ef);'."\n",'','','');
  72
  73 $derivative_func_interface=generate('    function_options & derivative_func(derivative_funcp_${N} d);'."\n",'','','');
  74
  75 $series_func_interface=generate('    function_options & series_func(series_funcp_${N} s);'."\n",'','','');
  76
  77 $print_func_interface=generate(
  78         <<'END_OF_PRINT_FUNC_INTERFACE','','','');
  79     template <class Ctx> function_options & print_func(print_funcp_${N} p)
  80     {
  81         test_and_set_nparams(${N});
  82         set_print_func(Ctx::get_class_info_static().options.get_id(), print_funcp(p));
  83         return *this;
  84     }
  85 END_OF_PRINT_FUNC_INTERFACE
  86
  87 $constructors_interface=generate(
  88 '    function(unsigned ser, ${SEQ1});'."\n",
  89 'const ex & param${N}','','');
  90
  91 $constructors_implementation=generate(
  92         <<'END_OF_CONSTRUCTORS_IMPLEMENTATION','const ex & param${N}','param${N}','');
  93 function::function(unsigned ser, ${SEQ1})
  94         : exprseq(${SEQ2}), serial(ser)
  95 {
  96         tinfo_key = TINFO_function;
  97 }
  98 END_OF_CONSTRUCTORS_IMPLEMENTATION
  99
 100 $eval_switch_statement=generate(
 101         <<'END_OF_EVAL_SWITCH_STATEMENT','seq[${N}-1]','','');
 102         case ${N}:
 103                 eval_result = ((eval_funcp_${N})(opt.eval_f))(${SEQ1});
 104                 break;
 105 END_OF_EVAL_SWITCH_STATEMENT
 106
 107 $evalf_switch_statement=generate(
 108         <<'END_OF_EVALF_SWITCH_STATEMENT','eseq[${N}-1]','','');
 109         case ${N}:
 110                 return ((evalf_funcp_${N})(opt.evalf_f))(${SEQ1});
 111 END_OF_EVALF_SWITCH_STATEMENT
 112
 113 $diff_switch_statement=generate(
 114         <<'END_OF_DIFF_SWITCH_STATEMENT','seq[${N}-1]','','');
 115         case ${N}:
 116                 return ((derivative_funcp_${N})(opt.derivative_f))(${SEQ1},diff_param);
 117 END_OF_DIFF_SWITCH_STATEMENT
 118
 119 $series_switch_statement=generate(
 120         <<'END_OF_SERIES_SWITCH_STATEMENT','seq[${N}-1]','','');
 121         case ${N}:
 122                 try {
 123                         res = ((series_funcp_${N})(opt.series_f))(${SEQ1},r,order,options);
 124                 } catch (do_taylor) {
 125                         res = basic::series(r, order, options);
 126                 }
 127                 return res;
 128 END_OF_SERIES_SWITCH_STATEMENT
 129
 130 $print_switch_statement=generate(
 131         <<'END_OF_PRINT_SWITCH_STATEMENT','seq[${N}-1]','','');
 132                 case ${N}:
 133                         ((print_funcp_${N})(pdt[id]))(${SEQ1}, c);
 134                         break;
 135 END_OF_PRINT_SWITCH_STATEMENT
 136
 137 $eval_func_implementation=generate(
 138         <<'END_OF_EVAL_FUNC_IMPLEMENTATION','','','');
 139 function_options & function_options::eval_func(eval_funcp_${N} e)
 140 {
 141         test_and_set_nparams(${N});
 142         eval_f = eval_funcp(e);
 143         return *this;
 144 }
 145 END_OF_EVAL_FUNC_IMPLEMENTATION
 146
 147 $evalf_func_implementation=generate(
 148         <<'END_OF_EVALF_FUNC_IMPLEMENTATION','','','');
 149 function_options & function_options::evalf_func(evalf_funcp_${N} ef)
 150 {
 151         test_and_set_nparams(${N});
 152         evalf_f = evalf_funcp(ef);
 153         return *this;
 154 }
 155 END_OF_EVALF_FUNC_IMPLEMENTATION
 156
 157 $derivative_func_implementation=generate(
 158         <<'END_OF_DERIVATIVE_FUNC_IMPLEMENTATION','','','');
 159 function_options & function_options::derivative_func(derivative_funcp_${N} d)
 160 {
 161         test_and_set_nparams(${N});
 162         derivative_f = derivative_funcp(d);
 163         return *this;
 164 }
 165 END_OF_DERIVATIVE_FUNC_IMPLEMENTATION
 166
 167 $series_func_implementation=generate(
 168         <<'END_OF_SERIES_FUNC_IMPLEMENTATION','','','');
 169 function_options & function_options::series_func(series_funcp_${N} s)
 170 {
 171         test_and_set_nparams(${N});
 172         series_f = series_funcp(s);
 173         return *this;
 174 }
 175 END_OF_SERIES_FUNC_IMPLEMENTATION
 176
 177 $interface=<<END_OF_INTERFACE;
 178 /** \@file function.h
 179  *
 180  *  Interface to class of symbolic functions. */
 181
 182 /*
 183  *  This file was generated automatically by function.pl.
 184  *  Please do not modify it directly, edit the perl script instead!
 185  *  function.pl options: \$maxargs=${maxargs}
 186  *
 187  *  GiNaC Copyright (C) 1999-2003 Johannes Gutenberg University Mainz, Germany
 188  *
 189  *  This program is free software; you can redistribute it and/or modify
 190  *  it under the terms of the GNU General Public License as published by
 191  *  the Free Software Foundation; either version 2 of the License, or
 192  *  (at your option) any later version.
 193  *
 194  *  This program is distributed in the hope that it will be useful,
 195  *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 196  *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 197  *  GNU General Public License for more details.
 198  *
 199  *  You should have received a copy of the GNU General Public License
 200  *  along with this program; if not, write to the Free Software
 201  *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 202  */
 203
 204 #ifndef __GINAC_FUNCTION_H__
 205 #define __GINAC_FUNCTION_H__
 206
 207 #include <string>
 208 #include <vector>
 209
 210 // CINT needs <algorithm> to work properly with <vector>
 211 #include <algorithm>
 212
 213 #include "exprseq.h"
 214
 215 // the following lines have been generated for max. ${maxargs} parameters
 216 $declare_function_macro
 217 // end of generated lines
 218
 219 #define REGISTER_FUNCTION(NAME,OPT) \\
 220 unsigned NAME##_SERIAL::serial = \\
 221         GiNaC::function::register_new(GiNaC::function_options(#NAME).OPT);
 222
 223 namespace GiNaC {
 224
 225 class function;
 226 class symmetry;
 227
 228 typedef ex (* eval_funcp)();
 229 typedef ex (* evalf_funcp)();
 230 typedef ex (* derivative_funcp)();
 231 typedef ex (* series_funcp)();
 232 typedef void (* print_funcp)();
 233
 234 // the following lines have been generated for max. ${maxargs} parameters
 235 $typedef_eval_funcp
 236 $typedef_evalf_funcp
 237 $typedef_derivative_funcp
 238 $typedef_series_funcp
 239 $typedef_print_funcp
 240 // end of generated lines
 241
 242 // Alternatively, an exvector may be passed into the static function, instead
 243 // of individual ex objects.  Then, the number of arguments is not limited.
 244 typedef ex (* eval_funcp_exvector)(const exvector &);
 245 typedef ex (* evalf_funcp_exvector)(const exvector &);
 246 typedef ex (* derivative_funcp_exvector)(const exvector &, unsigned);
 247 typedef ex (* series_funcp_exvector)(const exvector &, const relational &, int, unsigned);
 248 typedef void (* print_funcp_exvector)(const exvector &, const print_context &);
 249
 250
 251 class function_options
 252 {
 253         friend class function;
 254         friend class fderivative;
 255 public:
 256         function_options();
 257         function_options(std::string const & n, std::string const & tn=std::string());
 258         ~function_options();
 259         void initialize();
 260         function_options & set_name(std::string const & n, std::string const & tn=std::string());
 261         function_options & latex_name(std::string const & tn);
 262 // the following lines have been generated for max. ${maxargs} parameters
 263 $eval_func_interface
 264 $evalf_func_interface
 265 $derivative_func_interface
 266 $series_func_interface
 267 $print_func_interface
 268 // end of generated lines
 269         function_options & eval_func(eval_funcp_exvector e);
 270         function_options & evalf_func(evalf_funcp_exvector ef);
 271         function_options & derivative_func(derivative_funcp_exvector d);
 272         function_options & series_func(series_funcp_exvector s);
 273
 274         template <class Ctx> function_options & print_func(print_funcp_exvector p)
 275         {
 276                 print_use_exvector_args = true;
 277                 set_print_func(Ctx::get_class_info_static().options.get_id(), print_funcp(p));
 278                 return *this;
 279         }
 280
 281         function_options & set_return_type(unsigned rt, unsigned rtt=0);
 282         function_options & do_not_evalf_params();
 283         function_options & remember(unsigned size, unsigned assoc_size=0,
 284                                     unsigned strategy=remember_strategies::delete_never);
 285         function_options & overloaded(unsigned o);
 286         function_options & set_symmetry(const symmetry & s);
 287
 288         std::string get_name() const { return name; }
 289         unsigned get_nparams() const { return nparams; }
 290
 291 protected:
 292         bool has_derivative() const { return derivative_f != NULL; }
 293         void test_and_set_nparams(unsigned n);
 294         void set_print_func(unsigned id, print_funcp f);
 295
 296         std::string name;
 297         std::string TeX_name;
 298
 299         unsigned nparams;
 300
 301         eval_funcp eval_f;
 302         evalf_funcp evalf_f;
 303         derivative_funcp derivative_f;
 304         series_funcp series_f;
 305         std::vector<print_funcp> print_dispatch_table;
 306
 307         bool evalf_params_first;
 308
 309         bool use_return_type;
 310         unsigned return_type;
 311         unsigned return_type_tinfo;
 312
 313         bool use_remember;
 314         unsigned remember_size;
 315         unsigned remember_assoc_size;
 316         unsigned remember_strategy;
 317
 318         bool eval_use_exvector_args;
 319         bool evalf_use_exvector_args;
 320         bool derivative_use_exvector_args;
 321         bool series_use_exvector_args;
 322         bool print_use_exvector_args;
 323
 324         unsigned functions_with_same_name;
 325
 326         ex symtree;
 327 };
 328
 329
 330 /** Exception class thrown by classes which provide their own series expansion
 331  *  to signal that ordinary Taylor expansion is safe. */
 332 class do_taylor {};
 333
 334
 335 /** The class function is used to implement builtin functions like sin, cos...
 336         and user defined functions */
 337 class function : public exprseq
 338 {
 339         GINAC_DECLARE_REGISTERED_CLASS(function, exprseq)
 340
 341         // CINT has a linking problem
 342 #ifndef __MAKECINT__
 343         friend void ginsh_get_ginac_functions();
 344 #endif // def __MAKECINT__
 345
 346         friend class remember_table_entry;
 347         // friend class remember_table_list;
 348         // friend class remember_table;
 349
 350 // member functions
 351
 352         // other constructors
 353 public:
 354         function(unsigned ser);
 355         // the following lines have been generated for max. ${maxargs} parameters
 356 $constructors_interface
 357         // end of generated lines
 358         function(unsigned ser, const exprseq & es);
 359         function(unsigned ser, const exvector & v, bool discardable = false);
 360         function(unsigned ser, exvector * vp); // vp will be deleted
 361
 362         // functions overriding virtual functions from base classes
 363 public:
 364         void print(const print_context & c, unsigned level = 0) const;
 365         unsigned precedence() const {return 70;}
 366         ex expand(unsigned options=0) const;
 367         ex eval(int level=0) const;
 368         ex evalf(int level=0) const;
 369         unsigned calchash() const;
 370         ex series(const relational & r, int order, unsigned options = 0) const;
 371         ex thiscontainer(const exvector & v) const;
 372         ex thiscontainer(exvector * vp) const;
 373 protected:
 374         ex derivative(const symbol & s) const;
 375         bool is_equal_same_type(const basic & other) const;
 376         bool match_same_type(const basic & other) const;
 377         unsigned return_type() const;
 378         unsigned return_type_tinfo() const;
 379
 380         // new virtual functions which can be overridden by derived classes
 381         // none
 382
 383         // non-virtual functions in this class
 384 protected:
 385         ex pderivative(unsigned diff_param) const; // partial differentiation
 386         static std::vector<function_options> & registered_functions();
 387         bool lookup_remember_table(ex & result) const;
 388         void store_remember_table(ex const & result) const;
 389 public:
 390         static unsigned register_new(function_options const & opt);
 391         static unsigned current_serial;
 392         static unsigned find_function(const std::string &name, unsigned nparams);
 393         unsigned get_serial() const {return serial;}
 394         std::string get_name() const;
 395
 396 // member variables
 397
 398 protected:
 399         unsigned serial;
 400 };
 401
 402 // utility functions/macros
 403
 404 /** Specialization of is_exactly_a<function>(obj) for objects of type function. */
 405 template<> inline bool is_exactly_a<function>(const basic & obj)
 406 {
 407         return obj.tinfo()==TINFO_function;
 408 }
 409
 410 template <typename T>
 411 inline bool is_the_function(const ex & x)
 412 {
 413         return is_exactly_a<function>(x)
 414             && ex_to<function>(x).get_serial() == T::serial;
 415 }
 416
 417 // Check whether OBJ is the specified symbolic function.
 418 #define is_ex_the_function(OBJ, FUNCNAME) (GiNaC::is_the_function<FUNCNAME##_SERIAL>(OBJ))
 419
 420 } // namespace GiNaC
 421
 422 #endif // ndef __GINAC_FUNCTION_H__
 423
 424 END_OF_INTERFACE
 425
 426 $implementation=<<END_OF_IMPLEMENTATION;
 427 /** \@file function.cpp
 428  *
 429  *  Implementation of class of symbolic functions. */
 430
 431 /*
 432  *  This file was generated automatically by function.pl.
 433  *  Please do not modify it directly, edit the perl script instead!
 434  *  function.pl options: \$maxargs=${maxargs}
 435  *
 436  *  GiNaC Copyright (C) 1999-2003 Johannes Gutenberg University Mainz, Germany
 437  *
 438  *  This program is free software; you can redistribute it and/or modify
 439  *  it under the terms of the GNU General Public License as published by
 440  *  the Free Software Foundation; either version 2 of the License, or
 441  *  (at your option) any later version.
 442  *
 443  *  This program is distributed in the hope that it will be useful,
 444  *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 445  *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 446  *  GNU General Public License for more details.
 447  *
 448  *  You should have received a copy of the GNU General Public License
 449  *  along with this program; if not, write to the Free Software
 450  *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 451  */
 452
 453 #include <iostream>
 454 #include <string>
 455 #include <stdexcept>
 456 #include <list>
 457
 458 #include "function.h"
 459 #include "operators.h"
 460 #include "fderivative.h"
 461 #include "ex.h"
 462 #include "lst.h"
 463 #include "symmetry.h"
 464 #include "print.h"
 465 #include "archive.h"
 466 #include "inifcns.h"
 467 #include "tostring.h"
 468 #include "utils.h"
 469 #include "remember.h"
 470
 471 namespace GiNaC {
 472
 473 //////////
 474 // helper class function_options
 475 //////////
 476
 477 function_options::function_options()
 478 {
 479         initialize();
 480 }
 481
 482 function_options::function_options(std::string const & n, std::string const & tn)
 483 {
 484         initialize();
 485         set_name(n,tn);
 486 }
 487
 488 function_options::~function_options()
 489 {
 490         // nothing to clean up at the moment
 491 }
 492
 493 void function_options::initialize()
 494 {
 495         set_name("unnamed_function","\\\\mbox{unnamed}");
 496         nparams = 0;
 497         eval_f = evalf_f = derivative_f = series_f = 0;
 498         evalf_params_first = true;
 499         use_return_type = false;
 500         eval_use_exvector_args = false;
 501         evalf_use_exvector_args = false;
 502         derivative_use_exvector_args = false;
 503         series_use_exvector_args = false;
 504         print_use_exvector_args = false;
 505         use_remember = false;
 506         functions_with_same_name = 1;
 507         symtree = 0;
 508 }
 509
 510 function_options & function_options::set_name(std::string const & n,
 511                                               std::string const & tn)
 512 {
 513         name = n;
 514         if (tn==std::string())
 515                 TeX_name = "\\\\mbox{"+name+"}";
 516         else
 517                 TeX_name = tn;
 518         return *this;
 519 }
 520
 521 function_options & function_options::latex_name(std::string const & tn)
 522 {
 523         TeX_name = tn;
 524         return *this;
 525 }
 526
 527 // the following lines have been generated for max. ${maxargs} parameters
 528 $eval_func_implementation
 529 $evalf_func_implementation
 530 $derivative_func_implementation
 531 $series_func_implementation
 532 // end of generated lines
 533
 534 function_options& function_options::eval_func(eval_funcp_exvector e)
 535 {
 536         eval_use_exvector_args = true;
 537         eval_f = eval_funcp(e);
 538         return *this;
 539 }
 540 function_options& function_options::evalf_func(evalf_funcp_exvector ef)
 541 {
 542         evalf_use_exvector_args = true;
 543         evalf_f = evalf_funcp(ef);
 544         return *this;
 545 }
 546 function_options& function_options::derivative_func(derivative_funcp_exvector d)
 547 {
 548         derivative_use_exvector_args = true;
 549         derivative_f = derivative_funcp(d);
 550         return *this;
 551 }
 552 function_options& function_options::series_func(series_funcp_exvector s)
 553 {
 554         series_use_exvector_args = true;
 555         series_f = series_funcp(s);
 556         return *this;
 557 }
 558
 559 function_options & function_options::set_return_type(unsigned rt, unsigned rtt)
 560 {
 561         use_return_type = true;
 562         return_type = rt;
 563         return_type_tinfo = rtt;
 564         return *this;
 565 }
 566
 567 function_options & function_options::do_not_evalf_params()
 568 {
 569         evalf_params_first = false;
 570         return *this;
 571 }
 572
 573 function_options & function_options::remember(unsigned size,
 574                                               unsigned assoc_size,
 575                                               unsigned strategy)
 576 {
 577         use_remember = true;
 578         remember_size = size;
 579         remember_assoc_size = assoc_size;
 580         remember_strategy = strategy;
 581         return *this;
 582 }
 583
 584 function_options & function_options::overloaded(unsigned o)
 585 {
 586         functions_with_same_name = o;
 587         return *this;
 588 }
 589
 590 function_options & function_options::set_symmetry(const symmetry & s)
 591 {
 592         symtree = s;
 593         return *this;
 594 }
 595
 596 void function_options::test_and_set_nparams(unsigned n)
 597 {
 598         if (nparams==0) {
 599                 nparams = n;
 600         } else if (nparams!=n) {
 601                 // we do not throw an exception here because this code is
 602                 // usually executed before main(), so the exception could not
 603                 // be caught anyhow
 604                 std::cerr << "WARNING: " << name << "(): number of parameters ("
 605                           << n << ") differs from number set before ("
 606                           << nparams << ")" << std::endl;
 607         }
 608 }
 609
 610 void function_options::set_print_func(unsigned id, print_funcp f)
 611 {
 612         if (id >= print_dispatch_table.size())
 613                 print_dispatch_table.resize(id + 1);
 614         print_dispatch_table[id] = f;
 615 }
 616
 617 /** This can be used as a hook for external applications. */
 618 unsigned function::current_serial = 0;
 619
 620
 621 GINAC_IMPLEMENT_REGISTERED_CLASS(function, exprseq)
 622
 623 //////////
 624 // default constructor
 625 //////////
 626
 627 // public
 628
 629 function::function() : serial(0)
 630 {
 631         tinfo_key = TINFO_function;
 632 }
 633
 634 //////////
 635 // other constructors
 636 //////////
 637
 638 // public
 639
 640 function::function(unsigned ser) : serial(ser)
 641 {
 642         tinfo_key = TINFO_function;
 643 }
 644
 645 // the following lines have been generated for max. ${maxargs} parameters
 646 $constructors_implementation
 647 // end of generated lines
 648
 649 function::function(unsigned ser, const exprseq & es) : exprseq(es), serial(ser)
 650 {
 651         tinfo_key = TINFO_function;
 652
 653         // Force re-evaluation even if the exprseq was already evaluated
 654         // (the exprseq copy constructor copies the flags)
 655         clearflag(status_flags::evaluated);
 656 }
 657
 658 function::function(unsigned ser, const exvector & v, bool discardable)
 659   : exprseq(v,discardable), serial(ser)
 660 {
 661         tinfo_key = TINFO_function;
 662 }
 663
 664 function::function(unsigned ser, exvector * vp)
 665   : exprseq(vp), serial(ser)
 666 {
 667         tinfo_key = TINFO_function;
 668 }
 669
 670 //////////
 671 // archiving
 672 //////////
 673
 674 /** Construct object from archive_node. */
 675 function::function(const archive_node &n, lst &sym_lst) : inherited(n, sym_lst)
 676 {
 677         // Find serial number by function name
 678         std::string s;
 679         if (n.find_string("name", s)) {
 680                 unsigned int ser = 0;
 681                 std::vector<function_options>::const_iterator i = registered_functions().begin(), iend = registered_functions().end();
 682                 while (i != iend) {
 683                         if (s == i->name) {
 684                                 serial = ser;
 685                                 return;
 686                         }
 687                         ++i; ++ser;
 688                 }
 689                 throw (std::runtime_error("unknown function '" + s + "' in archive"));
 690         } else
 691                 throw (std::runtime_error("unnamed function in archive"));
 692 }
 693
 694 /** Unarchive the object. */
 695 ex function::unarchive(const archive_node &n, lst &sym_lst)
 696 {
 697         return (new function(n, sym_lst))->setflag(status_flags::dynallocated);
 698 }
 699
 700 /** Archive the object. */
 701 void function::archive(archive_node &n) const
 702 {
 703         inherited::archive(n);
 704         GINAC_ASSERT(serial < registered_functions().size());
 705         n.add_string("name", registered_functions()[serial].name);
 706 }
 707
 708 //////////
 709 // functions overriding virtual functions from base classes
 710 //////////
 711
 712 // public
 713
 714 void function::print(const print_context & c, unsigned level) const
 715 {
 716         GINAC_ASSERT(serial<registered_functions().size());
 717         const function_options &opt = registered_functions()[serial];
 718         const std::vector<print_funcp> &pdt = opt.print_dispatch_table;
 719
 720         // Dynamically dispatch on print_context type
 721         const print_context_class_info *pc_info = &c.get_class_info();
 722
 723 next_context:
 724         unsigned id = pc_info->options.get_id();
 725         if (id >= pdt.size() || pdt[id] == NULL) {
 726
 727                 // Method not found, try parent print_context class
 728                 const print_context_class_info *parent_pc_info = pc_info->get_parent();
 729                 if (parent_pc_info) {
 730                         pc_info = parent_pc_info;
 731                         goto next_context;
 732                 }
 733
 734                 // Method still not found, use default output
 735                 if (is_a<print_tree>(c)) {
 736
 737                         c.s << std::string(level, ' ') << class_name() << " "
 738                             << opt.name
 739                             << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
 740                             << ", nops=" << nops()
 741                             << std::endl;
 742                         unsigned delta_indent = static_cast<const print_tree &>(c).delta_indent;
 743                         for (size_t i=0; i<seq.size(); ++i)
 744                                 seq[i].print(c, level + delta_indent);
 745                         c.s << std::string(level + delta_indent, ' ') << "=====" << std::endl;
 746
 747                 } else if (is_a<print_csrc>(c)) {
 748
 749                         // Print function name in lowercase
 750                         std::string lname = opt.name;
 751                         size_t num = lname.size();
 752                         for (size_t i=0; i<num; i++)
 753                                 lname[i] = tolower(lname[i]);
 754                         c.s << lname;
 755                         printseq(c, '(', ',', ')', exprseq::precedence(), function::precedence());
 756
 757                 } else if (is_a<print_latex>(c)) {
 758                         c.s << opt.TeX_name;
 759                         printseq(c, '(', ',', ')', exprseq::precedence(), function::precedence());
 760                 } else {
 761                         c.s << opt.name;
 762                         printseq(c, '(', ',', ')', exprseq::precedence(), function::precedence());
 763                 }
 764
 765         } else {
 766
 767                 // Method found, call it
 768                 current_serial = serial;
 769                 if (opt.print_use_exvector_args)
 770                         ((print_funcp_exvector)pdt[id])(seq, c);
 771                 else switch (opt.nparams) {
 772                         // the following lines have been generated for max. ${maxargs} parameters
 773 ${print_switch_statement}
 774                         // end of generated lines
 775                 default:
 776                         throw(std::logic_error("function::print(): invalid nparams"));
 777                 }
 778         }
 779 }
 780
 781 ex function::expand(unsigned options) const
 782 {
 783         // Only expand arguments when asked to do so
 784         if (options & expand_options::expand_function_args)
 785                 return inherited::expand(options);
 786         else
 787                 return (options == 0) ? setflag(status_flags::expanded) : *this;
 788 }
 789
 790 ex function::eval(int level) const
 791 {
 792         if (level>1) {
 793                 // first evaluate children, then we will end up here again
 794                 return function(serial,evalchildren(level));
 795         }
 796
 797         GINAC_ASSERT(serial<registered_functions().size());
 798         const function_options &opt = registered_functions()[serial];
 799
 800         // Canonicalize argument order according to the symmetry properties
 801         if (seq.size() > 1 && !(opt.symtree.is_zero())) {
 802                 exvector v = seq;
 803                 GINAC_ASSERT(is_a<symmetry>(opt.symtree));
 804                 int sig = canonicalize(v.begin(), ex_to<symmetry>(opt.symtree));
 805                 if (sig != INT_MAX) {
 806                         // Something has changed while sorting arguments, more evaluations later
 807                         if (sig == 0)
 808                                 return _ex0;
 809                         return ex(sig) * thiscontainer(v);
 810                 }
 811         }
 812
 813         if (opt.eval_f==0) {
 814                 return this->hold();
 815         }
 816
 817         bool use_remember = opt.use_remember;
 818         ex eval_result;
 819         if (use_remember && lookup_remember_table(eval_result)) {
 820                 return eval_result;
 821         }
 822         current_serial = serial;
 823         if (opt.eval_use_exvector_args)
 824                 eval_result = ((eval_funcp_exvector)(opt.eval_f))(seq);
 825         else
 826         switch (opt.nparams) {
 827                 // the following lines have been generated for max. ${maxargs} parameters
 828 ${eval_switch_statement}
 829                 // end of generated lines
 830         default:
 831                 throw(std::logic_error("function::eval(): invalid nparams"));
 832         }
 833         if (use_remember) {
 834                 store_remember_table(eval_result);
 835         }
 836         return eval_result;
 837 }
 838
 839 ex function::evalf(int level) const
 840 {
 841         GINAC_ASSERT(serial<registered_functions().size());
 842         const function_options &opt = registered_functions()[serial];
 843
 844         // Evaluate children first
 845         exvector eseq;
 846         if (level == 1 || !(opt.evalf_params_first))
 847                 eseq = seq;
 848         else if (level == -max_recursion_level)
 849                 throw(std::runtime_error("max recursion level reached"));
 850         else {
 851                 eseq.reserve(seq.size());
 852                 --level;
 853                 exvector::const_iterator it = seq.begin(), itend = seq.end();
 854                 while (it != itend) {
 855                         eseq.push_back(it->evalf(level));
 856                         ++it;
 857                 }
 858         }
 859
 860         if (opt.evalf_f==0) {
 861                 return function(serial,eseq).hold();
 862         }
 863         current_serial = serial;
 864         if (opt.evalf_use_exvector_args)
 865                 return ((evalf_funcp_exvector)(opt.evalf_f))(seq);
 866         switch (opt.nparams) {
 867                 // the following lines have been generated for max. ${maxargs} parameters
 868 ${evalf_switch_statement}
 869                 // end of generated lines
 870         }
 871         throw(std::logic_error("function::evalf(): invalid nparams"));
 872 }
 873
 874 unsigned function::calchash() const
 875 {
 876         unsigned v = golden_ratio_hash(golden_ratio_hash(tinfo()) ^ serial);
 877         for (size_t i=0; i<nops(); i++) {
 878                 v = rotate_left(v);
 879                 v ^= this->op(i).gethash();
 880         }
 881
 882         if (flags & status_flags::evaluated) {
 883                 setflag(status_flags::hash_calculated);
 884                 hashvalue = v;
 885         }
 886         return v;
 887 }
 888
 889 ex function::thiscontainer(const exvector & v) const
 890 {
 891         return function(serial,v);
 892 }
 893
 894 ex function::thiscontainer(exvector * vp) const
 895 {
 896         return function(serial,vp);
 897 }
 898
 899 /** Implementation of ex::series for functions.
 900  *  \@see ex::series */
 901 ex function::series(const relational & r, int order, unsigned options) const
 902 {
 903         GINAC_ASSERT(serial<registered_functions().size());
 904         const function_options &opt = registered_functions()[serial];
 905
 906         if (opt.series_f==0) {
 907                 return basic::series(r, order);
 908         }
 909         ex res;
 910         current_serial = serial;
 911         if (opt.series_use_exvector_args) {
 912                 try {
 913                         res = ((series_funcp_exvector)(opt.series_f))(seq, r, order, options);
 914                 } catch (do_taylor) {
 915                         res = basic::series(r, order, options);
 916                 }
 917                 return res;
 918         }
 919         switch (opt.nparams) {
 920                 // the following lines have been generated for max. ${maxargs} parameters
 921 ${series_switch_statement}
 922                 // end of generated lines
 923         }
 924         throw(std::logic_error("function::series(): invalid nparams"));
 925 }
 926
 927 // protected
 928
 929 /** Implementation of ex::diff() for functions. It applies the chain rule,
 930  *  except for the Order term function.
 931  *  \@see ex::diff */
 932 ex function::derivative(const symbol & s) const
 933 {
 934         ex result;
 935
 936         if (serial == Order_SERIAL::serial) {
 937                 // Order Term function only differentiates the argument
 938                 return Order(seq[0].diff(s));
 939         } else {
 940                 // Chain rule
 941                 ex arg_diff;
 942                 size_t num = seq.size();
 943                 for (size_t i=0; i<num; i++) {
 944                         arg_diff = seq[i].diff(s);
 945                         // We apply the chain rule only when it makes sense.  This is not
 946                         // just for performance reasons but also to allow functions to
 947                         // throw when differentiated with respect to one of its arguments
 948                         // without running into trouble with our automatic full
 949                         // differentiation:
 950                         if (!arg_diff.is_zero())
 951                                 result += pderivative(i)*arg_diff;
 952                 }
 953         }
 954         return result;
 955 }
 956
 957 int function::compare_same_type(const basic & other) const
 958 {
 959         GINAC_ASSERT(is_a<function>(other));
 960         const function & o = static_cast<const function &>(other);
 961
 962         if (serial != o.serial)
 963                 return serial < o.serial ? -1 : 1;
 964         else
 965                 return exprseq::compare_same_type(o);
 966 }
 967
 968 bool function::is_equal_same_type(const basic & other) const
 969 {
 970         GINAC_ASSERT(is_a<function>(other));
 971         const function & o = static_cast<const function &>(other);
 972
 973         if (serial != o.serial)
 974                 return false;
 975         else
 976                 return exprseq::is_equal_same_type(o);
 977 }
 978
 979 bool function::match_same_type(const basic & other) const
 980 {
 981         GINAC_ASSERT(is_a<function>(other));
 982         const function & o = static_cast<const function &>(other);
 983
 984         return serial == o.serial;
 985 }
 986
 987 unsigned function::return_type() const
 988 {
 989         GINAC_ASSERT(serial<registered_functions().size());
 990         const function_options &opt = registered_functions()[serial];
 991
 992         if (opt.use_return_type) {
 993                 // Return type was explicitly specified
 994                 return opt.return_type;
 995         } else {
 996                 // Default behavior is to use the return type of the first
 997                 // argument. Thus, exp() of a matrix behaves like a matrix, etc.
 998                 if (seq.empty())
 999                         return return_types::commutative;
1000                 else
1001                         return seq.begin()->return_type();
1002         }
1003 }
1004
1005 unsigned function::return_type_tinfo() const
1006 {
1007         GINAC_ASSERT(serial<registered_functions().size());
1008         const function_options &opt = registered_functions()[serial];
1009
1010         if (opt.use_return_type) {
1011                 // Return type was explicitly specified
1012                 return opt.return_type_tinfo;
1013         } else {
1014                 // Default behavior is to use the return type of the first
1015                 // argument. Thus, exp() of a matrix behaves like a matrix, etc.
1016                 if (seq.empty())
1017                         return tinfo_key;
1018                 else
1019                         return seq.begin()->return_type_tinfo();
1020         }
1021 }
1022
1023 //////////
1024 // new virtual functions which can be overridden by derived classes
1025 //////////
1026
1027 // none
1028
1029 //////////
1030 // non-virtual functions in this class
1031 //////////
1032
1033 // protected
1034
1035 ex function::pderivative(unsigned diff_param) const // partial differentiation
1036 {
1037         GINAC_ASSERT(serial<registered_functions().size());
1038         const function_options &opt = registered_functions()[serial];
1039
1040         // No derivative defined? Then return abstract derivative object
1041         if (opt.derivative_f == NULL)
1042                 return fderivative(serial, diff_param, seq);
1043
1044         current_serial = serial;
1045         if (opt.derivative_use_exvector_args)
1046                 return ((derivative_funcp_exvector)(opt.derivative_f))(seq, diff_param);
1047         switch (opt.nparams) {
1048                 // the following lines have been generated for max. ${maxargs} parameters
1049 ${diff_switch_statement}
1050                 // end of generated lines
1051         }
1052         throw(std::logic_error("function::pderivative(): no diff function defined"));
1053 }
1054
1055 std::vector<function_options> & function::registered_functions()
1056 {
1057         static std::vector<function_options> * rf = new std::vector<function_options>;
1058         return *rf;
1059 }
1060
1061 bool function::lookup_remember_table(ex & result) const
1062 {
1063         return remember_table::remember_tables()[this->serial].lookup_entry(*this,result);
1064 }
1065
1066 void function::store_remember_table(ex const & result) const
1067 {
1068         remember_table::remember_tables()[this->serial].add_entry(*this,result);
1069 }
1070
1071 // public
1072
1073 unsigned function::register_new(function_options const & opt)
1074 {
1075         size_t same_name = 0;
1076         for (size_t i=0; i<registered_functions().size(); ++i) {
1077                 if (registered_functions()[i].name==opt.name) {
1078                         ++same_name;
1079                 }
1080         }
1081         if (same_name>=opt.functions_with_same_name) {
1082                 // we do not throw an exception here because this code is
1083                 // usually executed before main(), so the exception could not
1084                 // caught anyhow
1085                 std::cerr << "WARNING: function name " << opt.name
1086                           << " already in use!" << std::endl;
1087         }
1088         registered_functions().push_back(opt);
1089         if (opt.use_remember) {
1090                 remember_table::remember_tables().
1091                         push_back(remember_table(opt.remember_size,
1092                                                  opt.remember_assoc_size,
1093                                                  opt.remember_strategy));
1094         } else {
1095                 remember_table::remember_tables().push_back(remember_table());
1096         }
1097         return registered_functions().size()-1;
1098 }
1099
1100 /** Find serial number of function by name and number of parameters.
1101  *  Throws exception if function was not found. */
1102 unsigned function::find_function(const std::string &name, unsigned nparams)
1103 {
1104         std::vector<function_options>::const_iterator i = function::registered_functions().begin(), end = function::registered_functions().end();
1105         unsigned serial = 0;
1106         while (i != end) {
1107                 if (i->get_name() == name && i->get_nparams() == nparams)
1108                         return serial;
1109                 ++i;
1110                 ++serial;
1111         }
1112         throw (std::runtime_error("no function '" + name + "' with " + ToString(nparams) + " parameters defined"));
1113 }
1114
1115 /** Return the print name of the function. */
1116 std::string function::get_name() const
1117 {
1118         GINAC_ASSERT(serial<registered_functions().size());
1119         return registered_functions()[serial].name;
1120 }
1121
1122 } // namespace GiNaC
1123
1124 END_OF_IMPLEMENTATION
1125
1126 print "Creating interface file function.h...";
1127 open OUT,">function.h" or die "cannot open function.h";
1128 print OUT $interface;
1129 close OUT;
1130 print "ok.\n";
1131
1132 print "Creating implementation file function.cpp...";
1133 open OUT,">function.cpp" or die "cannot open function.cpp";
1134 print OUT $implementation;
1135 close OUT;
1136 print "ok.\n";
1137
1138 print "done.\n";