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,$from,$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                 $res .= eval('"' . $template . '"');
  26                 $SEQ1=''; # to avoid main::SEQ1 used only once warning
  27                 $SEQ2=''; # same as above
  28         }
  29         return $res;
  30 }
  31
  32 sub generate {
  33         my ($template,$seq_template1,$seq_template2)=@_;
  34         return generate_from_to($template,$seq_template1,$seq_template2,1,$maxargs);
  35 }
  36
  37 $declare_function_macro = <<'END_OF_DECLARE_FUNCTION_1_AND_2P_MACRO';
  38 #define DECLARE_FUNCTION_1P(NAME) \
  39 extern const unsigned function_index_##NAME; \
  40 inline GiNaC::function NAME(const GiNaC::ex & p1) { \
  41         return GiNaC::function(function_index_##NAME, p1); \
  42 }
  43 #define DECLARE_FUNCTION_2P(NAME) \
  44 extern const unsigned function_index_##NAME; \
  45 inline GiNaC::function NAME(const GiNaC::ex & p1, const GiNaC::ex & p2) { \
  46         return GiNaC::function(function_index_##NAME, p1, p2); \
  47 }
  48
  49 END_OF_DECLARE_FUNCTION_1_AND_2P_MACRO
  50
  51 $declare_function_macro .= generate_from_to(
  52         <<'END_OF_DECLARE_FUNCTION_MACRO','const GiNaC::ex & p${N}','p${N}',3,$maxargs);
  53 #define DECLARE_FUNCTION_${N}P(NAME) \\
  54 extern const unsigned function_index_##NAME; \\
  55 inline GiNaC::function NAME(${SEQ1}) { \\
  56         return GiNaC::function(function_index_##NAME, ${SEQ2}); \\
  57 }
  58
  59 END_OF_DECLARE_FUNCTION_MACRO
  60
  61 $typedef_eval_funcp=generate(
  62 'typedef ex (* eval_funcp_${N})(${SEQ1});'."\n",
  63 'const ex &','');
  64
  65 $typedef_evalf_funcp=generate(
  66 'typedef ex (* evalf_funcp_${N})(${SEQ1});'."\n",
  67 'const ex &','');
  68
  69 $typedef_derivative_funcp=generate(
  70 'typedef ex (* derivative_funcp_${N})(${SEQ1}, unsigned);'."\n",
  71 'const ex &','');
  72
  73 $typedef_series_funcp=generate(
  74 'typedef ex (* series_funcp_${N})(${SEQ1}, const relational &, int, unsigned);'."\n",
  75 'const ex &','');
  76
  77 $eval_func_interface=generate('    function_options & eval_func(eval_funcp_${N} e);'."\n",'','');
  78
  79 $evalf_func_interface=generate('    function_options & evalf_func(evalf_funcp_${N} ef);'."\n",'','');
  80
  81 $derivative_func_interface=generate('    function_options & derivative_func(derivative_funcp_${N} d);'."\n",'','');
  82
  83 $series_func_interface=generate('    function_options & series_func(series_funcp_${N} s);'."\n",'','');
  84
  85 $constructors_interface=generate(
  86 '    function(unsigned ser, ${SEQ1});'."\n",
  87 'const ex & param${N}','');
  88
  89 $constructors_implementation=generate(
  90         <<'END_OF_CONSTRUCTORS_IMPLEMENTATION','const ex & param${N}','param${N}');
  91 function::function(unsigned ser, ${SEQ1})
  92         : exprseq(${SEQ2}), serial(ser)
  93 {
  94         debugmsg(\"function ctor from unsigned,${N}*ex\",LOGLEVEL_CONSTRUCT);
  95         tinfo_key = TINFO_function;
  96 }
  97 END_OF_CONSTRUCTORS_IMPLEMENTATION
  98
  99 $eval_switch_statement=generate(
 100         <<'END_OF_EVAL_SWITCH_STATEMENT','seq[${N}-1]','');
 101         case ${N}:
 102                 eval_result=((eval_funcp_${N})(registered_functions()[serial].eval_f))(${SEQ1});
 103                 break;
 104 END_OF_EVAL_SWITCH_STATEMENT
 105
 106 $evalf_switch_statement=generate(
 107         <<'END_OF_EVALF_SWITCH_STATEMENT','eseq[${N}-1]','');
 108         case ${N}:
 109                 return ((evalf_funcp_${N})(registered_functions()[serial].evalf_f))(${SEQ1});
 110 END_OF_EVALF_SWITCH_STATEMENT
 111
 112 $diff_switch_statement=generate(
 113         <<'END_OF_DIFF_SWITCH_STATEMENT','seq[${N}-1]','');
 114         case ${N}:
 115                 return ((derivative_funcp_${N})(registered_functions()[serial].derivative_f))(${SEQ1},diff_param);
 116 END_OF_DIFF_SWITCH_STATEMENT
 117
 118 $series_switch_statement=generate(
 119         <<'END_OF_SERIES_SWITCH_STATEMENT','seq[${N}-1]','');
 120         case ${N}:
 121                 try {
 122                         res = ((series_funcp_${N})(registered_functions()[serial].series_f))(${SEQ1},r,order,options);
 123                 } catch (do_taylor) {
 124                         res = basic::series(r, order, options);
 125                 }
 126                 return res;
 127 END_OF_SERIES_SWITCH_STATEMENT
 128
 129 $eval_func_implementation=generate(
 130         <<'END_OF_EVAL_FUNC_IMPLEMENTATION','','');
 131 function_options & function_options::eval_func(eval_funcp_${N} e)
 132 {
 133         test_and_set_nparams(${N});
 134         eval_f=eval_funcp(e);
 135         return *this;
 136 }
 137 END_OF_EVAL_FUNC_IMPLEMENTATION
 138
 139 $evalf_func_implementation=generate(
 140         <<'END_OF_EVALF_FUNC_IMPLEMENTATION','','');
 141 function_options & function_options::evalf_func(evalf_funcp_${N} ef)
 142 {
 143         test_and_set_nparams(${N});
 144         evalf_f=evalf_funcp(ef);
 145         return *this;
 146 }
 147 END_OF_EVALF_FUNC_IMPLEMENTATION
 148
 149 $derivative_func_implementation=generate(
 150         <<'END_OF_DERIVATIVE_FUNC_IMPLEMENTATION','','');
 151 function_options & function_options::derivative_func(derivative_funcp_${N} d)
 152 {
 153         test_and_set_nparams(${N});
 154         derivative_f=derivative_funcp(d);
 155         return *this;
 156 }
 157 END_OF_DERIVATIVE_FUNC_IMPLEMENTATION
 158
 159 $series_func_implementation=generate(
 160         <<'END_OF_SERIES_FUNC_IMPLEMENTATION','','');
 161 function_options & function_options::series_func(series_funcp_${N} s)
 162 {
 163         test_and_set_nparams(${N});
 164         series_f=series_funcp(s);
 165         return *this;
 166 }
 167 END_OF_SERIES_FUNC_IMPLEMENTATION
 168
 169 $interface=<<END_OF_INTERFACE;
 170 /** \@file function.h
 171  *
 172  *  Interface to abstract class function (new function concept). */
 173
 174 /*
 175  *  This file was generated automatically by function.pl.
 176  *  Please do not modify it directly, edit the perl script instead!
 177  *  function.pl options: \$maxargs=${maxargs}
 178  *
 179  *  GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
 180  *
 181  *  This program is free software; you can redistribute it and/or modify
 182  *  it under the terms of the GNU General Public License as published by
 183  *  the Free Software Foundation; either version 2 of the License, or
 184  *  (at your option) any later version.
 185  *
 186  *  This program is distributed in the hope that it will be useful,
 187  *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 188  *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 189  *  GNU General Public License for more details.
 190  *
 191  *  You should have received a copy of the GNU General Public License
 192  *  along with this program; if not, write to the Free Software
 193  *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 194  */
 195
 196 #ifndef __GINAC_FUNCTION_H__
 197 #define __GINAC_FUNCTION_H__
 198
 199 #include <string>
 200 #include <vector>
 201
 202 // CINT needs <algorithm> to work properly with <vector>
 203 #include <algorithm>
 204
 205 #include "exprseq.h"
 206
 207 // the following lines have been generated for max. ${maxargs} parameters
 208 $declare_function_macro
 209 // end of generated lines
 210
 211 #define REGISTER_FUNCTION(NAME,OPT) \\
 212 const unsigned function_index_##NAME= \\
 213         GiNaC::function::register_new(GiNaC::function_options(#NAME).OPT);
 214
 215 #define REGISTER_FUNCTION_OLD(NAME,E,EF,D,S) \\
 216 const unsigned function_index_##NAME= \\
 217         GiNaC::function::register_new(GiNaC::function_options(#NAME). \\
 218                                       eval_func(E). \\
 219                                       evalf_func(EF). \\
 220                                       derivative_func(D). \\
 221                                       series_func(S));
 222
 223 #define BEGIN_TYPECHECK \\
 224 bool automatic_typecheck=true;
 225
 226 #define TYPECHECK(VAR,TYPE) \\
 227 if (!is_ex_exactly_of_type(VAR,TYPE)) { \\
 228         automatic_typecheck=false; \\
 229 } else
 230
 231 #define TYPECHECK_INTEGER(VAR) \\
 232 if (!(VAR).info(GiNaC::info_flags::integer)) { \\
 233         automatic_typecheck=false; \\
 234 } else
 235
 236 #define END_TYPECHECK(RV) \\
 237 {} \\
 238 if (!automatic_typecheck) { \\
 239         return RV.hold(); \\
 240 }
 241
 242 namespace GiNaC {
 243
 244 class function;
 245 class symmetry;
 246
 247 typedef ex (* eval_funcp)();
 248 typedef ex (* evalf_funcp)();
 249 typedef ex (* derivative_funcp)();
 250 typedef ex (* series_funcp)();
 251
 252 // the following lines have been generated for max. ${maxargs} parameters
 253 $typedef_eval_funcp
 254 $typedef_evalf_funcp
 255 $typedef_derivative_funcp
 256 $typedef_series_funcp
 257 // end of generated lines
 258
 259 class function_options
 260 {
 261         friend class function;
 262 public:
 263         function_options();
 264         function_options(std::string const & n, std::string const & tn=std::string());
 265         ~function_options();
 266         void initialize(void);
 267         function_options & set_name(std::string const & n, std::string const & tn=std::string());
 268         function_options & latex_name(std::string const & tn);
 269 // the following lines have been generated for max. ${maxargs} parameters
 270 $eval_func_interface
 271 $evalf_func_interface
 272 $derivative_func_interface
 273 $series_func_interface
 274 // end of generated lines
 275         function_options & set_return_type(unsigned rt, unsigned rtt=0);
 276         function_options & do_not_evalf_params(void);
 277         function_options & remember(unsigned size, unsigned assoc_size=0,
 278                                     unsigned strategy=remember_strategies::delete_never);
 279         function_options & overloaded(unsigned o);
 280         function_options & set_symmetry(const symmetry & s);
 281         void test_and_set_nparams(unsigned n);
 282         std::string get_name(void) const { return name; }
 283         unsigned get_nparams(void) const { return nparams; }
 284
 285 protected:
 286         std::string name;
 287         std::string TeX_name;
 288
 289         unsigned nparams;
 290
 291         eval_funcp eval_f;
 292         evalf_funcp evalf_f;
 293         derivative_funcp derivative_f;
 294         series_funcp series_f;
 295
 296         bool evalf_params_first;
 297
 298         bool use_return_type;
 299         unsigned return_type;
 300         unsigned return_type_tinfo;
 301
 302         bool use_remember;
 303         unsigned remember_size;
 304         unsigned remember_assoc_size;
 305         unsigned remember_strategy;
 306
 307         unsigned functions_with_same_name;
 308
 309         ex symtree;
 310 };
 311
 312 /** The class function is used to implement builtin functions like sin, cos...
 313         and user defined functions */
 314 class function : public exprseq
 315 {
 316         GINAC_DECLARE_REGISTERED_CLASS(function, exprseq)
 317
 318         // CINT has a linking problem
 319 #ifndef __MAKECINT__
 320         friend void ginsh_get_ginac_functions(void);
 321 #endif // def __MAKECINT__
 322
 323         friend class remember_table_entry;
 324         // friend class remember_table_list;
 325         // friend class remember_table;
 326
 327 // member functions
 328
 329         // other ctors
 330 public:
 331         function(unsigned ser);
 332         // the following lines have been generated for max. ${maxargs} parameters
 333 $constructors_interface
 334         // end of generated lines
 335         function(unsigned ser, const exprseq & es);
 336         function(unsigned ser, const exvector & v, bool discardable=0);
 337         function(unsigned ser, exvector * vp); // vp will be deleted
 338
 339         // functions overriding virtual functions from bases classes
 340 public:
 341         void print(const print_context & c, unsigned level = 0) const;
 342         unsigned precedence(void) const {return 70;}
 343         int degree(const ex & s) const;
 344         int ldegree(const ex & s) const;
 345         ex coeff(const ex & s, int n = 1) const;
 346         ex expand(unsigned options=0) const;
 347         ex eval(int level=0) const;
 348         ex evalf(int level=0) const;
 349         unsigned calchash(void) const;
 350         ex series(const relational & r, int order, unsigned options = 0) const;
 351         bool match(const ex & pattern, lst & repl_lst) const;
 352         ex thisexprseq(const exvector & v) const;
 353         ex thisexprseq(exvector * vp) const;
 354 protected:
 355         ex derivative(const symbol & s) const;
 356         bool is_equal_same_type(const basic & other) const;
 357         unsigned return_type(void) const;
 358         unsigned return_type_tinfo(void) const;
 359
 360         // new virtual functions which can be overridden by derived classes
 361         // none
 362
 363         // non-virtual functions in this class
 364 protected:
 365         ex pderivative(unsigned diff_param) const; // partial differentiation
 366         static std::vector<function_options> & registered_functions(void);
 367         bool lookup_remember_table(ex & result) const;
 368         void store_remember_table(ex const & result) const;
 369 public:
 370         static unsigned register_new(function_options const & opt);
 371         static unsigned find_function(const std::string &name, unsigned nparams);
 372         unsigned get_serial(void) const {return serial;}
 373         std::string get_name(void) const;
 374
 375 // member variables
 376
 377 protected:
 378         unsigned serial;
 379 };
 380
 381 // utility functions/macros
 382 inline const function &ex_to_function(const ex &e)
 383 {
 384         return static_cast<const function &>(*e.bp);
 385 }
 386
 387 #define is_ex_the_function(OBJ, FUNCNAME) \\
 388         (is_ex_exactly_of_type(OBJ, function) && static_cast<GiNaC::function *>(OBJ.bp)->get_serial() == function_index_##FUNCNAME)
 389
 390 } // namespace GiNaC
 391
 392 #endif // ndef __GINAC_FUNCTION_H__
 393
 394 END_OF_INTERFACE
 395
 396 $implementation=<<END_OF_IMPLEMENTATION;
 397 /** \@file function.cpp
 398  *
 399  *  Implementation of class function. */
 400
 401 /*
 402  *  This file was generated automatically by function.pl.
 403  *  Please do not modify it directly, edit the perl script instead!
 404  *  function.pl options: \$maxargs=${maxargs}
 405  *
 406  *  GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
 407  *
 408  *  This program is free software; you can redistribute it and/or modify
 409  *  it under the terms of the GNU General Public License as published by
 410  *  the Free Software Foundation; either version 2 of the License, or
 411  *  (at your option) any later version.
 412  *
 413  *  This program is distributed in the hope that it will be useful,
 414  *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 415  *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 416  *  GNU General Public License for more details.
 417  *
 418  *  You should have received a copy of the GNU General Public License
 419  *  along with this program; if not, write to the Free Software
 420  *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 421  */
 422
 423 #include <string>
 424 #include <stdexcept>
 425 #include <list>
 426
 427 #include "function.h"
 428 #include "ex.h"
 429 #include "lst.h"
 430 #include "symmetry.h"
 431 #include "print.h"
 432 #include "archive.h"
 433 #include "inifcns.h"
 434 #include "utils.h"
 435 #include "debugmsg.h"
 436 #include "remember.h"
 437
 438 namespace GiNaC {
 439
 440 //////////
 441 // helper class function_options
 442 //////////
 443
 444 function_options::function_options()
 445 {
 446         initialize();
 447 }
 448
 449 function_options::function_options(std::string const & n, std::string const & tn)
 450 {
 451         initialize();
 452         set_name(n,tn);
 453 }
 454
 455 function_options::~function_options()
 456 {
 457         // nothing to clean up at the moment
 458 }
 459
 460 void function_options::initialize(void)
 461 {
 462         set_name("unnamed_function","\\\\mbox{unnamed}");
 463         nparams=0;
 464         eval_f=evalf_f=derivative_f=series_f=0;
 465         evalf_params_first=true;
 466         use_return_type=false;
 467         use_remember=false;
 468         functions_with_same_name=1;
 469         symtree = 0;
 470 }
 471
 472 function_options & function_options::set_name(std::string const & n,
 473                                               std::string const & tn)
 474 {
 475         name=n;
 476         if (tn==std::string()) {
 477                 TeX_name="\\\\mbox{"+name+"}";
 478         } else {
 479                 TeX_name=tn;
 480         }
 481         return *this;
 482 }
 483
 484 function_options & function_options::latex_name(std::string const & tn)
 485 {
 486         TeX_name=tn;
 487         return *this;
 488 }
 489
 490 // the following lines have been generated for max. ${maxargs} parameters
 491 $eval_func_implementation
 492 $evalf_func_implementation
 493 $derivative_func_implementation
 494 $series_func_implementation
 495 // end of generated lines
 496
 497 function_options & function_options::set_return_type(unsigned rt, unsigned rtt)
 498 {
 499         use_return_type=true;
 500         return_type=rt;
 501         return_type_tinfo=rtt;
 502         return *this;
 503 }
 504
 505 function_options & function_options::do_not_evalf_params(void)
 506 {
 507         evalf_params_first=false;
 508         return *this;
 509 }
 510
 511 function_options & function_options::remember(unsigned size,
 512                                               unsigned assoc_size,
 513                                               unsigned strategy)
 514 {
 515         use_remember=true;
 516         remember_size=size;
 517         remember_assoc_size=assoc_size;
 518         remember_strategy=strategy;
 519         return *this;
 520 }
 521
 522 function_options & function_options::overloaded(unsigned o)
 523 {
 524         functions_with_same_name=o;
 525         return *this;
 526 }
 527
 528 function_options & function_options::set_symmetry(const symmetry & s)
 529 {
 530         symtree = s;
 531         return *this;
 532 }
 533
 534 void function_options::test_and_set_nparams(unsigned n)
 535 {
 536         if (nparams==0) {
 537                 nparams=n;
 538         } else if (nparams!=n) {
 539                 // we do not throw an exception here because this code is
 540                 // usually executed before main(), so the exception could not
 541                 // caught anyhow
 542                 std::cerr << "WARNING: number of parameters ("
 543                           << n << ") differs from number set before ("
 544                           << nparams << ")" << std::endl;
 545         }
 546 }
 547
 548 GINAC_IMPLEMENT_REGISTERED_CLASS(function, exprseq)
 549
 550 //////////
 551 // default ctor, dtor, copy ctor assignment operator and helpers
 552 //////////
 553
 554 // public
 555
 556 function::function() : serial(0)
 557 {
 558         debugmsg("function default ctor",LOGLEVEL_CONSTRUCT);
 559         tinfo_key = TINFO_function;
 560 }
 561
 562 // protected
 563
 564 void function::copy(const function & other)
 565 {
 566         exprseq::copy(other);
 567         serial=other.serial;
 568 }
 569
 570 void function::destroy(bool call_parent)
 571 {
 572         if (call_parent) exprseq::destroy(call_parent);
 573 }
 574
 575 //////////
 576 // other ctors
 577 //////////
 578
 579 // public
 580
 581 function::function(unsigned ser) : serial(ser)
 582 {
 583         debugmsg("function ctor from unsigned",LOGLEVEL_CONSTRUCT);
 584         tinfo_key = TINFO_function;
 585 }
 586
 587 // the following lines have been generated for max. ${maxargs} parameters
 588 $constructors_implementation
 589 // end of generated lines
 590
 591 function::function(unsigned ser, const exprseq & es) : exprseq(es), serial(ser)
 592 {
 593         debugmsg("function ctor from unsigned,exprseq",LOGLEVEL_CONSTRUCT);
 594         tinfo_key = TINFO_function;
 595 }
 596
 597 function::function(unsigned ser, const exvector & v, bool discardable)
 598   : exprseq(v,discardable), serial(ser)
 599 {
 600         debugmsg("function ctor from string,exvector,bool",LOGLEVEL_CONSTRUCT);
 601         tinfo_key = TINFO_function;
 602 }
 603
 604 function::function(unsigned ser, exvector * vp)
 605   : exprseq(vp), serial(ser)
 606 {
 607         debugmsg("function ctor from unsigned,exvector *",LOGLEVEL_CONSTRUCT);
 608         tinfo_key = TINFO_function;
 609 }
 610
 611 //////////
 612 // archiving
 613 //////////
 614
 615 /** Construct object from archive_node. */
 616 function::function(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
 617 {
 618         debugmsg("function ctor from archive_node", LOGLEVEL_CONSTRUCT);
 619
 620         // Find serial number by function name
 621         std::string s;
 622         if (n.find_string("name", s)) {
 623                 unsigned int ser = 0;
 624                 std::vector<function_options>::const_iterator i = registered_functions().begin(), iend = registered_functions().end();
 625                 while (i != iend) {
 626                         if (s == i->name) {
 627                                 serial = ser;
 628                                 return;
 629                         }
 630                         i++; ser++;
 631                 }
 632                 throw (std::runtime_error("unknown function '" + s + "' in archive"));
 633         } else
 634                 throw (std::runtime_error("unnamed function in archive"));
 635 }
 636
 637 /** Unarchive the object. */
 638 ex function::unarchive(const archive_node &n, const lst &sym_lst)
 639 {
 640         return (new function(n, sym_lst))->setflag(status_flags::dynallocated);
 641 }
 642
 643 /** Archive the object. */
 644 void function::archive(archive_node &n) const
 645 {
 646         inherited::archive(n);
 647         GINAC_ASSERT(serial < registered_functions().size());
 648         n.add_string("name", registered_functions()[serial].name);
 649 }
 650
 651 //////////
 652 // functions overriding virtual functions from bases classes
 653 //////////
 654
 655 // public
 656
 657 void function::print(const print_context & c, unsigned level) const
 658 {
 659         debugmsg("function print", LOGLEVEL_PRINT);
 660
 661         GINAC_ASSERT(serial<registered_functions().size());
 662
 663         if (is_of_type(c, print_tree)) {
 664
 665                 c.s << std::string(level, ' ') << class_name() << " "
 666                     << registered_functions()[serial].name
 667                     << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
 668                     << ", nops=" << nops()
 669                     << std::endl;
 670                 unsigned delta_indent = static_cast<const print_tree &>(c).delta_indent;
 671                 for (unsigned i=0; i<nops(); ++i)
 672                         seq[i].print(c, level + delta_indent);
 673                 c.s << std::string(level + delta_indent, ' ') << "=====" << std::endl;
 674
 675         } else if (is_of_type(c, print_csrc)) {
 676
 677                 // Print function name in lowercase
 678                 std::string lname = registered_functions()[serial].name;
 679                 for (unsigned i=0; i<lname.size(); i++)
 680                         lname[i] = tolower(lname[i]);
 681                 c.s << lname << "(";
 682
 683                 // Print arguments, separated by commas
 684                 exvector::const_iterator it = seq.begin(), itend = seq.end();
 685                 while (it != itend) {
 686                         it->print(c);
 687                         it++;
 688                         if (it != itend)
 689                                 c.s << ",";
 690                 }
 691                 c.s << ")";
 692
 693         } else if (is_of_type(c, print_latex)) {
 694                 c.s << registered_functions()[serial].TeX_name;
 695                 printseq(c, '(', ',', ')', exprseq::precedence(), function::precedence());
 696         } else {
 697                 c.s << registered_functions()[serial].name;
 698                 printseq(c, '(', ',', ')', exprseq::precedence(), function::precedence());
 699         }
 700 }
 701
 702 ex function::expand(unsigned options) const
 703 {
 704         return this->setflag(status_flags::expanded);
 705 }
 706
 707 int function::degree(const ex & s) const
 708 {
 709         return is_equal(*s.bp) ? 1 : 0;
 710 }
 711
 712 int function::ldegree(const ex & s) const
 713 {
 714         return is_equal(*s.bp) ? 1 : 0;
 715 }
 716
 717 ex function::coeff(const ex & s, int n) const
 718 {
 719         if (is_equal(*s.bp))
 720                 return n==1 ? _ex1() : _ex0();
 721         else
 722                 return n==0 ? ex(*this) : _ex0();
 723 }
 724
 725 ex function::eval(int level) const
 726 {
 727         GINAC_ASSERT(serial<registered_functions().size());
 728
 729         if (level>1) {
 730                 // first evaluate children, then we will end up here again
 731                 return function(serial,evalchildren(level));
 732         }
 733
 734         const function_options &opt = registered_functions()[serial];
 735
 736         // Canonicalize argument order according to the symmetry properties
 737         if (seq.size() > 1 && !(opt.symtree.is_zero())) {
 738                 exvector v = seq;
 739                 GINAC_ASSERT(is_ex_exactly_of_type(opt.symtree, symmetry));
 740                 int sig = canonicalize(v.begin(), ex_to_symmetry(opt.symtree));
 741                 if (sig != INT_MAX) {
 742                         // Something has changed while sorting arguments, more evaluations later
 743                         if (sig == 0)
 744                                 return _ex0();
 745                         return ex(sig) * thisexprseq(v);
 746                 }
 747         }
 748
 749         if (opt.eval_f==0) {
 750                 return this->hold();
 751         }
 752
 753         bool use_remember=opt.use_remember;
 754         ex eval_result;
 755         if (use_remember && lookup_remember_table(eval_result)) {
 756                 return eval_result;
 757         }
 758
 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         exvector eseq=evalfchildren(level);
 777
 778         if (registered_functions()[serial].evalf_f==0) {
 779                 return function(serial,eseq).hold();
 780         }
 781         switch (registered_functions()[serial].nparams) {
 782                 // the following lines have been generated for max. ${maxargs} parameters
 783 ${evalf_switch_statement}
 784                 // end of generated lines
 785         }
 786         throw(std::logic_error("function::evalf(): invalid nparams"));
 787 }
 788
 789 unsigned function::calchash(void) const
 790 {
 791         unsigned v = golden_ratio_hash(golden_ratio_hash(tinfo()) ^ serial);
 792         for (unsigned i=0; i<nops(); i++) {
 793                 v = rotate_left_31(v);
 794                 v ^= this->op(i).gethash();
 795         }
 796         v &= 0x7FFFFFFFU;
 797         if (flags & status_flags::evaluated) {
 798                 setflag(status_flags::hash_calculated);
 799                 hashvalue = v;
 800         }
 801         return v;
 802 }
 803
 804 ex function::thisexprseq(const exvector & v) const
 805 {
 806         return function(serial,v);
 807 }
 808
 809 ex function::thisexprseq(exvector * vp) const
 810 {
 811         return function(serial,vp);
 812 }
 813
 814 /** Implementation of ex::series for functions.
 815  *  \@see ex::series */
 816 ex function::series(const relational & r, int order, unsigned options) const
 817 {
 818         GINAC_ASSERT(serial<registered_functions().size());
 819
 820         if (registered_functions()[serial].series_f==0) {
 821                 return basic::series(r, order);
 822         }
 823         ex res;
 824         switch (registered_functions()[serial].nparams) {
 825                 // the following lines have been generated for max. ${maxargs} parameters
 826 ${series_switch_statement}
 827                 // end of generated lines
 828         }
 829         throw(std::logic_error("function::series(): invalid nparams"));
 830 }
 831
 832 bool function::match(const ex & pattern, lst & repl_lst) const
 833 {
 834         // Serial number must match
 835         if (is_ex_of_type(pattern, function) && serial != ex_to_function(pattern).serial)
 836                 return false;
 837         return inherited::match(pattern, repl_lst);
 838 }
 839
 840 // protected
 841
 842
 843 /** Implementation of ex::diff() for functions. It applies the chain rule,
 844  *  except for the Order term function.
 845  *  \@see ex::diff */
 846 ex function::derivative(const symbol & s) const
 847 {
 848         ex result;
 849
 850         if (serial == function_index_Order) {
 851                 // Order Term function only differentiates the argument
 852                 return Order(seq[0].diff(s));
 853         } else if (serial == function_index_Derivative) {
 854                 // Inert derivative performs chain rule on the first argument only, and
 855                 // adds differentiation parameter to list (second argument)
 856                 GINAC_ASSERT(is_ex_exactly_of_type(seq[0], function));
 857                 GINAC_ASSERT(is_ex_exactly_of_type(seq[1], function));
 858                 ex fcn = seq[0];
 859                 ex arg_diff;
 860                 for (unsigned i=0; i!=fcn.nops(); i++) {
 861                         arg_diff = fcn.op(i).diff(s);
 862                         if (!arg_diff.is_zero()) {
 863                                 lst new_lst = ex_to_lst(seq[1]);
 864                                 new_lst.append(i);
 865                                 result += arg_diff * Derivative(fcn, new_lst);
 866                         }
 867                 }
 868         } else {
 869                 // Chain rule
 870                 ex arg_diff;
 871                 for (unsigned i=0; i!=seq.size(); i++) {
 872                         arg_diff = seq[i].diff(s);
 873                         // We apply the chain rule only when it makes sense.  This is not
 874                         // just for performance reasons but also to allow functions to
 875                         // throw when differentiated with respect to one of its arguments
 876                         // without running into trouble with our automatic full
 877                         // differentiation:
 878                         if (!arg_diff.is_zero())
 879                                 result += pderivative(i)*arg_diff;
 880                 }
 881         }
 882         return result;
 883 }
 884
 885 int function::compare_same_type(const basic & other) const
 886 {
 887         GINAC_ASSERT(is_of_type(other, function));
 888         const function & o=static_cast<function &>(const_cast<basic &>(other));
 889
 890         if (serial!=o.serial) {
 891                 return serial < o.serial ? -1 : 1;
 892         }
 893         return exprseq::compare_same_type(o);
 894 }
 895
 896 bool function::is_equal_same_type(const basic & other) const
 897 {
 898         GINAC_ASSERT(is_of_type(other, function));
 899         const function & o=static_cast<function &>(const_cast<basic &>(other));
 900
 901         if (serial!=o.serial) return false;
 902         return exprseq::is_equal_same_type(o);
 903 }
 904
 905 unsigned function::return_type(void) const
 906 {
 907         if (seq.size()==0) {
 908                 return return_types::commutative;
 909         }
 910         return (*seq.begin()).return_type();
 911 }
 912
 913 unsigned function::return_type_tinfo(void) const
 914 {
 915         if (seq.size()==0) {
 916                 return tinfo_key;
 917         }
 918         return (*seq.begin()).return_type_tinfo();
 919 }
 920
 921 //////////
 922 // new virtual functions which can be overridden by derived classes
 923 //////////
 924
 925 // none
 926
 927 //////////
 928 // non-virtual functions in this class
 929 //////////
 930
 931 // protected
 932
 933 ex function::pderivative(unsigned diff_param) const // partial differentiation
 934 {
 935         GINAC_ASSERT(serial<registered_functions().size());
 936
 937         if (registered_functions()[serial].derivative_f==0) {
 938                 return Derivative(*this, lst(ex(diff_param)));
 939         }
 940         switch (registered_functions()[serial].nparams) {
 941                 // the following lines have been generated for max. ${maxargs} parameters
 942 ${diff_switch_statement}
 943                 // end of generated lines
 944         }
 945         throw(std::logic_error("function::pderivative(): no diff function defined"));
 946 }
 947
 948 std::vector<function_options> & function::registered_functions(void)
 949 {
 950         static std::vector<function_options> * rf = new std::vector<function_options>;
 951         return *rf;
 952 }
 953
 954 bool function::lookup_remember_table(ex & result) const
 955 {
 956         return remember_table::remember_tables()[serial].lookup_entry(*this,result);
 957 }
 958
 959 void function::store_remember_table(ex const & result) const
 960 {
 961         remember_table::remember_tables()[serial].add_entry(*this,result);
 962 }
 963
 964 // public
 965
 966 unsigned function::register_new(function_options const & opt)
 967 {
 968         unsigned same_name=0;
 969         for (unsigned i=0; i<registered_functions().size(); ++i) {
 970                 if (registered_functions()[i].name==opt.name) {
 971                         same_name++;
 972                 }
 973         }
 974         if (same_name>=opt.functions_with_same_name) {
 975                 // we do not throw an exception here because this code is
 976                 // usually executed before main(), so the exception could not
 977                 // caught anyhow
 978                 std::cerr << "WARNING: function name " << opt.name
 979                                   << " already in use!" << std::endl;
 980         }
 981         registered_functions().push_back(opt);
 982         if (opt.use_remember) {
 983                 remember_table::remember_tables().
 984                         push_back(remember_table(opt.remember_size,
 985                                                                          opt.remember_assoc_size,
 986                                                                          opt.remember_strategy));
 987         } else {
 988                 remember_table::remember_tables().push_back(remember_table());
 989         }
 990         return registered_functions().size()-1;
 991 }
 992
 993 /** Find serial number of function by name and number of parameters.
 994  *  Throws exception if function was not found. */
 995 unsigned function::find_function(const std::string &name, unsigned nparams)
 996 {
 997         std::vector<function_options>::const_iterator i = function::registered_functions().begin(), end = function::registered_functions().end();
 998         unsigned serial = 0;
 999         while (i != end) {
1000                 if (i->get_name() == name && i->get_nparams() == nparams)
1001                         return serial;
1002                 i++;
1003                 serial++;
1004         }
1005         throw (std::runtime_error("no function '" + name + "' with " + ToString(nparams) + " parameters defined"));
1006 }
1007
1008 /** Return the print name of the function. */
1009 std::string function::get_name(void) const
1010 {
1011         GINAC_ASSERT(serial<registered_functions().size());
1012         return registered_functions()[serial].name;
1013 }
1014
1015 } // namespace GiNaC
1016
1017 END_OF_IMPLEMENTATION
1018
1019 print "Creating interface file function.h...";
1020 open OUT,">function.h" or die "cannot open function.h";
1021 print OUT $interface;
1022 close OUT;
1023 print "ok.\n";
1024
1025 print "Creating implementation file function.cpp...";
1026 open OUT,">function.cpp" or die "cannot open function.cpp";
1027 print OUT $implementation;
1028 close OUT;
1029 print "ok.\n";
1030
1031 print "done.\n";