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 $declare_function_macro = generate_from_to(
  38         <<'END_OF_DECLARE_FUNCTION_MACRO','const GiNaC::ex & p${N}','p${N}',1,$maxargs);
  39 #define DECLARE_FUNCTION_${N}P(NAME) \\
  40 extern const unsigned function_index_##NAME; \\
  41 inline const GiNaC::function NAME(${SEQ1}) { \\
  42         return GiNaC::function(function_index_##NAME, ${SEQ2}); \\
  43 }
  44
  45 END_OF_DECLARE_FUNCTION_MACRO
  46
  47 $typedef_eval_funcp=generate(
  48 'typedef ex (* eval_funcp_${N})(${SEQ1});'."\n",
  49 'const ex &','');
  50
  51 $typedef_evalf_funcp=generate(
  52 'typedef ex (* evalf_funcp_${N})(${SEQ1});'."\n",
  53 'const ex &','');
  54
  55 $typedef_derivative_funcp=generate(
  56 'typedef ex (* derivative_funcp_${N})(${SEQ1}, unsigned);'."\n",
  57 'const ex &','');
  58
  59 $typedef_series_funcp=generate(
  60 'typedef ex (* series_funcp_${N})(${SEQ1}, const relational &, int, unsigned);'."\n",
  61 'const ex &','');
  62
  63 $eval_func_interface=generate('    function_options & eval_func(eval_funcp_${N} e);'."\n",'','');
  64
  65 $evalf_func_interface=generate('    function_options & evalf_func(evalf_funcp_${N} ef);'."\n",'','');
  66
  67 $derivative_func_interface=generate('    function_options & derivative_func(derivative_funcp_${N} d);'."\n",'','');
  68
  69 $series_func_interface=generate('    function_options & series_func(series_funcp_${N} s);'."\n",'','');
  70
  71 $constructors_interface=generate(
  72 '    function(unsigned ser, ${SEQ1});'."\n",
  73 'const ex & param${N}','');
  74
  75 $constructors_implementation=generate(
  76         <<'END_OF_CONSTRUCTORS_IMPLEMENTATION','const ex & param${N}','param${N}');
  77 function::function(unsigned ser, ${SEQ1})
  78         : exprseq(${SEQ2}), serial(ser)
  79 {
  80         debugmsg(\"function ctor from unsigned,${N}*ex\",LOGLEVEL_CONSTRUCT);
  81         tinfo_key = TINFO_function;
  82 }
  83 END_OF_CONSTRUCTORS_IMPLEMENTATION
  84
  85 $eval_switch_statement=generate(
  86         <<'END_OF_EVAL_SWITCH_STATEMENT','seq[${N}-1]','');
  87         case ${N}:
  88                 eval_result = ((eval_funcp_${N})(registered_functions()[serial].eval_f))(${SEQ1});
  89                 break;
  90 END_OF_EVAL_SWITCH_STATEMENT
  91
  92 $evalf_switch_statement=generate(
  93         <<'END_OF_EVALF_SWITCH_STATEMENT','eseq[${N}-1]','');
  94         case ${N}:
  95                 return ((evalf_funcp_${N})(registered_functions()[serial].evalf_f))(${SEQ1});
  96 END_OF_EVALF_SWITCH_STATEMENT
  97
  98 $diff_switch_statement=generate(
  99         <<'END_OF_DIFF_SWITCH_STATEMENT','seq[${N}-1]','');
 100         case ${N}:
 101                 return ((derivative_funcp_${N})(registered_functions()[serial].derivative_f))(${SEQ1},diff_param);
 102 END_OF_DIFF_SWITCH_STATEMENT
 103
 104 $series_switch_statement=generate(
 105         <<'END_OF_SERIES_SWITCH_STATEMENT','seq[${N}-1]','');
 106         case ${N}:
 107                 try {
 108                         res = ((series_funcp_${N})(registered_functions()[serial].series_f))(${SEQ1},r,order,options);
 109                 } catch (do_taylor) {
 110                         res = basic::series(r, order, options);
 111                 }
 112                 return res;
 113 END_OF_SERIES_SWITCH_STATEMENT
 114
 115 $eval_func_implementation=generate(
 116         <<'END_OF_EVAL_FUNC_IMPLEMENTATION','','');
 117 function_options & function_options::eval_func(eval_funcp_${N} e)
 118 {
 119         test_and_set_nparams(${N});
 120         eval_f = eval_funcp(e);
 121         return *this;
 122 }
 123 END_OF_EVAL_FUNC_IMPLEMENTATION
 124
 125 $evalf_func_implementation=generate(
 126         <<'END_OF_EVALF_FUNC_IMPLEMENTATION','','');
 127 function_options & function_options::evalf_func(evalf_funcp_${N} ef)
 128 {
 129         test_and_set_nparams(${N});
 130         evalf_f = evalf_funcp(ef);
 131         return *this;
 132 }
 133 END_OF_EVALF_FUNC_IMPLEMENTATION
 134
 135 $derivative_func_implementation=generate(
 136         <<'END_OF_DERIVATIVE_FUNC_IMPLEMENTATION','','');
 137 function_options & function_options::derivative_func(derivative_funcp_${N} d)
 138 {
 139         test_and_set_nparams(${N});
 140         derivative_f = derivative_funcp(d);
 141         return *this;
 142 }
 143 END_OF_DERIVATIVE_FUNC_IMPLEMENTATION
 144
 145 $series_func_implementation=generate(
 146         <<'END_OF_SERIES_FUNC_IMPLEMENTATION','','');
 147 function_options & function_options::series_func(series_funcp_${N} s)
 148 {
 149         test_and_set_nparams(${N});
 150         series_f = series_funcp(s);
 151         return *this;
 152 }
 153 END_OF_SERIES_FUNC_IMPLEMENTATION
 154
 155 $interface=<<END_OF_INTERFACE;
 156 /** \@file function.h
 157  *
 158  *  Interface to abstract class function (new function concept). */
 159
 160 /*
 161  *  This file was generated automatically by function.pl.
 162  *  Please do not modify it directly, edit the perl script instead!
 163  *  function.pl options: \$maxargs=${maxargs}
 164  *
 165  *  GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
 166  *
 167  *  This program is free software; you can redistribute it and/or modify
 168  *  it under the terms of the GNU General Public License as published by
 169  *  the Free Software Foundation; either version 2 of the License, or
 170  *  (at your option) any later version.
 171  *
 172  *  This program is distributed in the hope that it will be useful,
 173  *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 174  *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 175  *  GNU General Public License for more details.
 176  *
 177  *  You should have received a copy of the GNU General Public License
 178  *  along with this program; if not, write to the Free Software
 179  *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 180  */
 181
 182 #ifndef __GINAC_FUNCTION_H__
 183 #define __GINAC_FUNCTION_H__
 184
 185 #include <string>
 186 #include <vector>
 187
 188 // CINT needs <algorithm> to work properly with <vector>
 189 #include <algorithm>
 190
 191 #include "exprseq.h"
 192
 193 // the following lines have been generated for max. ${maxargs} parameters
 194 $declare_function_macro
 195 // end of generated lines
 196
 197 #define REGISTER_FUNCTION(NAME,OPT) \\
 198 const unsigned function_index_##NAME= \\
 199         GiNaC::function::register_new(GiNaC::function_options(#NAME).OPT);
 200
 201 #define BEGIN_TYPECHECK \\
 202 bool automatic_typecheck=true;
 203
 204 #define TYPECHECK(VAR,TYPE) \\
 205 if (!is_exactly_a<TYPE>(VAR)) { \\
 206         automatic_typecheck=false; \\
 207 } else
 208
 209 #define TYPECHECK_INTEGER(VAR) \\
 210 if (!(VAR).info(GiNaC::info_flags::integer)) { \\
 211         automatic_typecheck=false; \\
 212 } else
 213
 214 #define END_TYPECHECK(RV) \\
 215 {} \\
 216 if (!automatic_typecheck) { \\
 217         return RV.hold(); \\
 218 }
 219
 220 namespace GiNaC {
 221
 222 class function;
 223 class symmetry;
 224
 225 typedef ex (* eval_funcp)();
 226 typedef ex (* evalf_funcp)();
 227 typedef ex (* derivative_funcp)();
 228 typedef ex (* series_funcp)();
 229
 230 // the following lines have been generated for max. ${maxargs} parameters
 231 $typedef_eval_funcp
 232 $typedef_evalf_funcp
 233 $typedef_derivative_funcp
 234 $typedef_series_funcp
 235 // end of generated lines
 236
 237 class function_options
 238 {
 239         friend class function;
 240 public:
 241         function_options();
 242         function_options(std::string const & n, std::string const & tn=std::string());
 243         ~function_options();
 244         void initialize(void);
 245         function_options & set_name(std::string const & n, std::string const & tn=std::string());
 246         function_options & latex_name(std::string const & tn);
 247 // the following lines have been generated for max. ${maxargs} parameters
 248 $eval_func_interface
 249 $evalf_func_interface
 250 $derivative_func_interface
 251 $series_func_interface
 252 // end of generated lines
 253         function_options & set_return_type(unsigned rt, unsigned rtt=0);
 254         function_options & do_not_evalf_params(void);
 255         function_options & remember(unsigned size, unsigned assoc_size=0,
 256                                     unsigned strategy=remember_strategies::delete_never);
 257         function_options & overloaded(unsigned o);
 258         function_options & set_symmetry(const symmetry & s);
 259         void test_and_set_nparams(unsigned n);
 260         std::string get_name(void) const { return name; }
 261         unsigned get_nparams(void) const { return nparams; }
 262         bool has_derivative(void) const { return derivative_f != NULL; }
 263
 264 protected:
 265         std::string name;
 266         std::string TeX_name;
 267
 268         unsigned nparams;
 269
 270         eval_funcp eval_f;
 271         evalf_funcp evalf_f;
 272         derivative_funcp derivative_f;
 273         series_funcp series_f;
 274
 275         bool evalf_params_first;
 276
 277         bool use_return_type;
 278         unsigned return_type;
 279         unsigned return_type_tinfo;
 280
 281         bool use_remember;
 282         unsigned remember_size;
 283         unsigned remember_assoc_size;
 284         unsigned remember_strategy;
 285
 286         unsigned functions_with_same_name;
 287
 288         ex symtree;
 289 };
 290
 291 /** The class function is used to implement builtin functions like sin, cos...
 292         and user defined functions */
 293 class function : public exprseq
 294 {
 295         GINAC_DECLARE_REGISTERED_CLASS(function, exprseq)
 296
 297         // CINT has a linking problem
 298 #ifndef __MAKECINT__
 299         friend void ginsh_get_ginac_functions(void);
 300 #endif // def __MAKECINT__
 301
 302         friend class remember_table_entry;
 303         // friend class remember_table_list;
 304         // friend class remember_table;
 305         friend ex Derivative_eval(const ex &, const ex &);
 306
 307 // member functions
 308
 309         // other ctors
 310 public:
 311         function(unsigned ser);
 312         // the following lines have been generated for max. ${maxargs} parameters
 313 $constructors_interface
 314         // end of generated lines
 315         function(unsigned ser, const exprseq & es);
 316         function(unsigned ser, const exvector & v, bool discardable = false);
 317         function(unsigned ser, exvector * vp); // vp will be deleted
 318
 319         // functions overriding virtual functions from bases classes
 320 public:
 321         void print(const print_context & c, unsigned level = 0) const;
 322         unsigned precedence(void) const {return 70;}
 323         int degree(const ex & s) const;
 324         int ldegree(const ex & s) const;
 325         ex coeff(const ex & s, int n = 1) const;
 326         ex expand(unsigned options=0) const;
 327         ex eval(int level=0) const;
 328         ex evalf(int level=0) const;
 329         unsigned calchash(void) const;
 330         ex series(const relational & r, int order, unsigned options = 0) const;
 331         ex thisexprseq(const exvector & v) const;
 332         ex thisexprseq(exvector * vp) const;
 333 protected:
 334         ex derivative(const symbol & s) const;
 335         bool is_equal_same_type(const basic & other) const;
 336         bool match_same_type(const basic & other) const;
 337         unsigned return_type(void) const;
 338         unsigned return_type_tinfo(void) const;
 339
 340         // new virtual functions which can be overridden by derived classes
 341         // none
 342
 343         // non-virtual functions in this class
 344 protected:
 345         ex pderivative(unsigned diff_param) const; // partial differentiation
 346         static std::vector<function_options> & registered_functions(void);
 347         bool lookup_remember_table(ex & result) const;
 348         void store_remember_table(ex const & result) const;
 349 public:
 350         static unsigned register_new(function_options const & opt);
 351         static unsigned find_function(const std::string &name, unsigned nparams);
 352         unsigned get_serial(void) const {return serial;}
 353         std::string get_name(void) const;
 354
 355 // member variables
 356
 357 protected:
 358         unsigned serial;
 359 };
 360
 361 // utility functions/macros
 362 /** Return the object of type function handled by an ex.
 363  *  This is unsafe: you need to check the type first. */
 364 inline const function &ex_to_function(const ex &e)
 365 {
 366         return static_cast<const function &>(*e.bp);
 367 }
 368
 369 /** Specialization of is_exactly_a<function>(obj) for objects of type function. */
 370 template<> inline bool is_exactly_a<function>(const basic & obj)
 371 {
 372         return obj.tinfo()==TINFO_function;
 373 }
 374
 375 #define is_ex_the_function(OBJ, FUNCNAME) \\
 376         (is_ex_exactly_of_type(OBJ, function) && static_cast<GiNaC::function *>(OBJ.bp)->get_serial() == function_index_##FUNCNAME)
 377
 378 } // namespace GiNaC
 379
 380 #endif // ndef __GINAC_FUNCTION_H__
 381
 382 END_OF_INTERFACE
 383
 384 $implementation=<<END_OF_IMPLEMENTATION;
 385 /** \@file function.cpp
 386  *
 387  *  Implementation of class function. */
 388
 389 /*
 390  *  This file was generated automatically by function.pl.
 391  *  Please do not modify it directly, edit the perl script instead!
 392  *  function.pl options: \$maxargs=${maxargs}
 393  *
 394  *  GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
 395  *
 396  *  This program is free software; you can redistribute it and/or modify
 397  *  it under the terms of the GNU General Public License as published by
 398  *  the Free Software Foundation; either version 2 of the License, or
 399  *  (at your option) any later version.
 400  *
 401  *  This program is distributed in the hope that it will be useful,
 402  *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 403  *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 404  *  GNU General Public License for more details.
 405  *
 406  *  You should have received a copy of the GNU General Public License
 407  *  along with this program; if not, write to the Free Software
 408  *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 409  */
 410
 411 #include <string>
 412 #include <stdexcept>
 413 #include <list>
 414
 415 #include "function.h"
 416 #include "ex.h"
 417 #include "lst.h"
 418 #include "symmetry.h"
 419 #include "print.h"
 420 #include "archive.h"
 421 #include "inifcns.h"
 422 #include "utils.h"
 423 #include "debugmsg.h"
 424 #include "remember.h"
 425
 426 namespace GiNaC {
 427
 428 //////////
 429 // helper class function_options
 430 //////////
 431
 432 function_options::function_options()
 433 {
 434         initialize();
 435 }
 436
 437 function_options::function_options(std::string const & n, std::string const & tn)
 438 {
 439         initialize();
 440         set_name(n,tn);
 441 }
 442
 443 function_options::~function_options()
 444 {
 445         // nothing to clean up at the moment
 446 }
 447
 448 void function_options::initialize(void)
 449 {
 450         set_name("unnamed_function","\\\\mbox{unnamed}");
 451         nparams = 0;
 452         eval_f = evalf_f = derivative_f = series_f = 0;
 453         evalf_params_first = true;
 454         use_return_type = false;
 455         use_remember = false;
 456         functions_with_same_name = 1;
 457         symtree = 0;
 458 }
 459
 460 function_options & function_options::set_name(std::string const & n,
 461                                               std::string const & tn)
 462 {
 463         name=n;
 464         if (tn==std::string())
 465                 TeX_name = "\\\\mbox{"+name+"}";
 466         else
 467                 TeX_name = tn;
 468         return *this;
 469 }
 470
 471 function_options & function_options::latex_name(std::string const & tn)
 472 {
 473         TeX_name=tn;
 474         return *this;
 475 }
 476
 477 // the following lines have been generated for max. ${maxargs} parameters
 478 $eval_func_implementation
 479 $evalf_func_implementation
 480 $derivative_func_implementation
 481 $series_func_implementation
 482 // end of generated lines
 483
 484 function_options & function_options::set_return_type(unsigned rt, unsigned rtt)
 485 {
 486         use_return_type = true;
 487         return_type = rt;
 488         return_type_tinfo = rtt;
 489         return *this;
 490 }
 491
 492 function_options & function_options::do_not_evalf_params(void)
 493 {
 494         evalf_params_first = false;
 495         return *this;
 496 }
 497
 498 function_options & function_options::remember(unsigned size,
 499                                               unsigned assoc_size,
 500                                               unsigned strategy)
 501 {
 502         use_remember = true;
 503         remember_size = size;
 504         remember_assoc_size = assoc_size;
 505         remember_strategy = strategy;
 506         return *this;
 507 }
 508
 509 function_options & function_options::overloaded(unsigned o)
 510 {
 511         functions_with_same_name = o;
 512         return *this;
 513 }
 514
 515 function_options & function_options::set_symmetry(const symmetry & s)
 516 {
 517         symtree = s;
 518         return *this;
 519 }
 520
 521 void function_options::test_and_set_nparams(unsigned n)
 522 {
 523         if (nparams==0) {
 524                 nparams = n;
 525         } else if (nparams!=n) {
 526                 // we do not throw an exception here because this code is
 527                 // usually executed before main(), so the exception could not
 528                 // caught anyhow
 529                 std::cerr << "WARNING: number of parameters ("
 530                           << n << ") differs from number set before ("
 531                           << nparams << ")" << std::endl;
 532         }
 533 }
 534
 535 GINAC_IMPLEMENT_REGISTERED_CLASS(function, exprseq)
 536
 537 //////////
 538 // default ctor, dtor, copy ctor assignment operator and helpers
 539 //////////
 540
 541 // public
 542
 543 function::function() : serial(0)
 544 {
 545         debugmsg("function default ctor",LOGLEVEL_CONSTRUCT);
 546         tinfo_key = TINFO_function;
 547 }
 548
 549 // protected
 550
 551 void function::copy(const function & other)
 552 {
 553         inherited::copy(other);
 554         serial = other.serial;
 555 }
 556
 557 void function::destroy(bool call_parent)
 558 {
 559         if (call_parent)
 560                 inherited::destroy(call_parent);
 561 }
 562
 563 //////////
 564 // other ctors
 565 //////////
 566
 567 // public
 568
 569 function::function(unsigned ser) : serial(ser)
 570 {
 571         debugmsg("function ctor from unsigned",LOGLEVEL_CONSTRUCT);
 572         tinfo_key = TINFO_function;
 573 }
 574
 575 // the following lines have been generated for max. ${maxargs} parameters
 576 $constructors_implementation
 577 // end of generated lines
 578
 579 function::function(unsigned ser, const exprseq & es) : exprseq(es), serial(ser)
 580 {
 581         debugmsg("function ctor from unsigned,exprseq",LOGLEVEL_CONSTRUCT);
 582         tinfo_key = TINFO_function;
 583 }
 584
 585 function::function(unsigned ser, const exvector & v, bool discardable)
 586   : exprseq(v,discardable), serial(ser)
 587 {
 588         debugmsg("function ctor from string,exvector,bool",LOGLEVEL_CONSTRUCT);
 589         tinfo_key = TINFO_function;
 590 }
 591
 592 function::function(unsigned ser, exvector * vp)
 593   : exprseq(vp), serial(ser)
 594 {
 595         debugmsg("function ctor from unsigned,exvector *",LOGLEVEL_CONSTRUCT);
 596         tinfo_key = TINFO_function;
 597 }
 598
 599 //////////
 600 // archiving
 601 //////////
 602
 603 /** Construct object from archive_node. */
 604 function::function(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
 605 {
 606         debugmsg("function ctor from archive_node", LOGLEVEL_CONSTRUCT);
 607
 608         // Find serial number by function name
 609         std::string s;
 610         if (n.find_string("name", s)) {
 611                 unsigned int ser = 0;
 612                 std::vector<function_options>::const_iterator i = registered_functions().begin(), iend = registered_functions().end();
 613                 while (i != iend) {
 614                         if (s == i->name) {
 615                                 serial = ser;
 616                                 return;
 617                         }
 618                         ++i; ++ser;
 619                 }
 620                 throw (std::runtime_error("unknown function '" + s + "' in archive"));
 621         } else
 622                 throw (std::runtime_error("unnamed function in archive"));
 623 }
 624
 625 /** Unarchive the object. */
 626 ex function::unarchive(const archive_node &n, const lst &sym_lst)
 627 {
 628         return (new function(n, sym_lst))->setflag(status_flags::dynallocated);
 629 }
 630
 631 /** Archive the object. */
 632 void function::archive(archive_node &n) const
 633 {
 634         inherited::archive(n);
 635         GINAC_ASSERT(serial < registered_functions().size());
 636         n.add_string("name", registered_functions()[serial].name);
 637 }
 638
 639 //////////
 640 // functions overriding virtual functions from bases classes
 641 //////////
 642
 643 // public
 644
 645 void function::print(const print_context & c, unsigned level) const
 646 {
 647         debugmsg("function print", LOGLEVEL_PRINT);
 648
 649         GINAC_ASSERT(serial<registered_functions().size());
 650
 651         if (is_of_type(c, print_tree)) {
 652
 653                 c.s << std::string(level, ' ') << class_name() << " "
 654                     << registered_functions()[serial].name
 655                     << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
 656                     << ", nops=" << nops()
 657                     << std::endl;
 658                 unsigned delta_indent = static_cast<const print_tree &>(c).delta_indent;
 659                 for (unsigned i=0; i<seq.size(); ++i)
 660                         seq[i].print(c, level + delta_indent);
 661                 c.s << std::string(level + delta_indent, ' ') << "=====" << std::endl;
 662
 663         } else if (is_of_type(c, print_csrc)) {
 664
 665                 // Print function name in lowercase
 666                 std::string lname = registered_functions()[serial].name;
 667                 unsigned num = lname.size();
 668                 for (unsigned i=0; i<num; i++)
 669                         lname[i] = tolower(lname[i]);
 670                 c.s << lname << "(";
 671
 672                 // Print arguments, separated by commas
 673                 exvector::const_iterator it = seq.begin(), itend = seq.end();
 674                 while (it != itend) {
 675                         it->print(c);
 676                         ++it;
 677                         if (it != itend)
 678                                 c.s << ",";
 679                 }
 680                 c.s << ")";
 681
 682         } else if (is_of_type(c, print_latex)) {
 683                 c.s << registered_functions()[serial].TeX_name;
 684                 printseq(c, '(', ',', ')', exprseq::precedence(), function::precedence());
 685         } else {
 686                 c.s << registered_functions()[serial].name;
 687                 printseq(c, '(', ',', ')', exprseq::precedence(), function::precedence());
 688         }
 689 }
 690
 691 ex function::expand(unsigned options) const
 692 {
 693         // Only expand arguments when asked to do so
 694         if (options & expand_options::expand_function_args)
 695                 return inherited::expand(options);
 696         else
 697                 return (options == 0) ? setflag(status_flags::expanded) : *this;
 698 }
 699
 700 int function::degree(const ex & s) const
 701 {
 702         return is_equal(*s.bp) ? 1 : 0;
 703 }
 704
 705 int function::ldegree(const ex & s) const
 706 {
 707         return is_equal(*s.bp) ? 1 : 0;
 708 }
 709
 710 ex function::coeff(const ex & s, int n) const
 711 {
 712         if (is_equal(*s.bp))
 713                 return n==1 ? _ex1() : _ex0();
 714         else
 715                 return n==0 ? ex(*this) : _ex0();
 716 }
 717
 718 ex function::eval(int level) const
 719 {
 720         GINAC_ASSERT(serial<registered_functions().size());
 721
 722         if (level>1) {
 723                 // first evaluate children, then we will end up here again
 724                 return function(serial,evalchildren(level));
 725         }
 726
 727         const function_options &opt = registered_functions()[serial];
 728
 729         // Canonicalize argument order according to the symmetry properties
 730         if (seq.size() > 1 && !(opt.symtree.is_zero())) {
 731                 exvector v = seq;
 732                 GINAC_ASSERT(is_ex_exactly_of_type(opt.symtree, symmetry));
 733                 int sig = canonicalize(v.begin(), ex_to<symmetry>(opt.symtree));
 734                 if (sig != INT_MAX) {
 735                         // Something has changed while sorting arguments, more evaluations later
 736                         if (sig == 0)
 737                                 return _ex0();
 738                         return ex(sig) * thisexprseq(v);
 739                 }
 740         }
 741
 742         if (opt.eval_f==0) {
 743                 return this->hold();
 744         }
 745
 746         bool use_remember = opt.use_remember;
 747         ex eval_result;
 748         if (use_remember && lookup_remember_table(eval_result)) {
 749                 return eval_result;
 750         }
 751
 752         switch (opt.nparams) {
 753                 // the following lines have been generated for max. ${maxargs} parameters
 754 ${eval_switch_statement}
 755                 // end of generated lines
 756         default:
 757                 throw(std::logic_error("function::eval(): invalid nparams"));
 758         }
 759         if (use_remember) {
 760                 store_remember_table(eval_result);
 761         }
 762         return eval_result;
 763 }
 764
 765 ex function::evalf(int level) const
 766 {
 767         GINAC_ASSERT(serial<registered_functions().size());
 768
 769         // Evaluate children first
 770         exvector eseq;
 771         if (level == 1)
 772                 eseq = seq;
 773         else if (level == -max_recursion_level)
 774                 throw(std::runtime_error("max recursion level reached"));
 775         else
 776                 eseq.reserve(seq.size());
 777         --level;
 778         exvector::const_iterator it = seq.begin(), itend = seq.end();
 779         while (it != itend) {
 780                 eseq.push_back(it->evalf(level));
 781                 ++it;
 782         }
 783
 784         if (registered_functions()[serial].evalf_f==0) {
 785                 return function(serial,eseq).hold();
 786         }
 787         switch (registered_functions()[serial].nparams) {
 788                 // the following lines have been generated for max. ${maxargs} parameters
 789 ${evalf_switch_statement}
 790                 // end of generated lines
 791         }
 792         throw(std::logic_error("function::evalf(): invalid nparams"));
 793 }
 794
 795 unsigned function::calchash(void) const
 796 {
 797         unsigned v = golden_ratio_hash(golden_ratio_hash(tinfo()) ^ serial);
 798         for (unsigned i=0; i<nops(); i++) {
 799                 v = rotate_left_31(v);
 800                 v ^= this->op(i).gethash();
 801         }
 802         v &= 0x7FFFFFFFU;
 803         if (flags & status_flags::evaluated) {
 804                 setflag(status_flags::hash_calculated);
 805                 hashvalue = v;
 806         }
 807         return v;
 808 }
 809
 810 ex function::thisexprseq(const exvector & v) const
 811 {
 812         return function(serial,v);
 813 }
 814
 815 ex function::thisexprseq(exvector * vp) const
 816 {
 817         return function(serial,vp);
 818 }
 819
 820 /** Implementation of ex::series for functions.
 821  *  \@see ex::series */
 822 ex function::series(const relational & r, int order, unsigned options) const
 823 {
 824         GINAC_ASSERT(serial<registered_functions().size());
 825
 826         if (registered_functions()[serial].series_f==0) {
 827                 return basic::series(r, order);
 828         }
 829         ex res;
 830         switch (registered_functions()[serial].nparams) {
 831                 // the following lines have been generated for max. ${maxargs} parameters
 832 ${series_switch_statement}
 833                 // end of generated lines
 834         }
 835         throw(std::logic_error("function::series(): invalid nparams"));
 836 }
 837
 838 // protected
 839
 840 /** Implementation of ex::diff() for functions. It applies the chain rule,
 841  *  except for the Order term function.
 842  *  \@see ex::diff */
 843 ex function::derivative(const symbol & s) const
 844 {
 845         ex result;
 846
 847         if (serial == function_index_Order) {
 848                 // Order Term function only differentiates the argument
 849                 return Order(seq[0].diff(s));
 850         } else if (serial == function_index_Derivative) {
 851                 // Inert derivative performs chain rule on the first argument only, and
 852                 // adds differentiation parameter to list (second argument)
 853                 GINAC_ASSERT(is_ex_exactly_of_type(seq[0], function));
 854                 GINAC_ASSERT(is_ex_exactly_of_type(seq[1], function));
 855                 ex fcn = seq[0];
 856                 ex arg_diff;
 857                 for (unsigned i=0; i!=fcn.nops(); i++) {
 858                         arg_diff = fcn.op(i).diff(s);
 859                         if (!arg_diff.is_zero()) {
 860                                 lst new_lst = ex_to<lst>(seq[1]);
 861                                 new_lst.append(i);
 862                                 result += arg_diff * Derivative(fcn, new_lst);
 863                         }
 864                 }
 865         } else {
 866                 // Chain rule
 867                 ex arg_diff;
 868                 unsigned num = seq.size();
 869                 for (unsigned i=0; i<num; i++) {
 870                         arg_diff = seq[i].diff(s);
 871                         // We apply the chain rule only when it makes sense.  This is not
 872                         // just for performance reasons but also to allow functions to
 873                         // throw when differentiated with respect to one of its arguments
 874                         // without running into trouble with our automatic full
 875                         // differentiation:
 876                         if (!arg_diff.is_zero())
 877                                 result += pderivative(i)*arg_diff;
 878                 }
 879         }
 880         return result;
 881 }
 882
 883 int function::compare_same_type(const basic & other) const
 884 {
 885         GINAC_ASSERT(is_of_type(other, function));
 886         const function & o = static_cast<const function &>(other);
 887
 888         if (serial != o.serial)
 889                 return serial < o.serial ? -1 : 1;
 890         else
 891                 return exprseq::compare_same_type(o);
 892 }
 893
 894 bool function::is_equal_same_type(const basic & other) const
 895 {
 896         GINAC_ASSERT(is_of_type(other, function));
 897         const function & o = static_cast<const function &>(other);
 898
 899         if (serial != o.serial)
 900                 return false;
 901         else
 902                 return exprseq::is_equal_same_type(o);
 903 }
 904
 905 bool function::match_same_type(const basic & other) const
 906 {
 907         GINAC_ASSERT(is_of_type(other, function));
 908         const function & o = static_cast<const function &>(other);
 909
 910         return serial == o.serial;
 911 }
 912
 913 unsigned function::return_type(void) const
 914 {
 915         if (seq.empty())
 916                 return return_types::commutative;
 917         else
 918                 return seq.begin()->return_type();
 919 }
 920
 921 unsigned function::return_type_tinfo(void) const
 922 {
 923         if (seq.empty())
 924                 return tinfo_key;
 925         else
 926                 return seq.begin()->return_type_tinfo();
 927 }
 928
 929 //////////
 930 // new virtual functions which can be overridden by derived classes
 931 //////////
 932
 933 // none
 934
 935 //////////
 936 // non-virtual functions in this class
 937 //////////
 938
 939 // protected
 940
 941 ex function::pderivative(unsigned diff_param) const // partial differentiation
 942 {
 943         GINAC_ASSERT(serial<registered_functions().size());
 944
 945         if (registered_functions()[serial].derivative_f==0) {
 946                 return Derivative(*this, lst(ex(diff_param)));
 947         }
 948         switch (registered_functions()[serial].nparams) {
 949                 // the following lines have been generated for max. ${maxargs} parameters
 950 ${diff_switch_statement}
 951                 // end of generated lines
 952         }
 953         throw(std::logic_error("function::pderivative(): no diff function defined"));
 954 }
 955
 956 std::vector<function_options> & function::registered_functions(void)
 957 {
 958         static std::vector<function_options> * rf = new std::vector<function_options>;
 959         return *rf;
 960 }
 961
 962 bool function::lookup_remember_table(ex & result) const
 963 {
 964         return remember_table::remember_tables()[serial].lookup_entry(*this,result);
 965 }
 966
 967 void function::store_remember_table(ex const & result) const
 968 {
 969         remember_table::remember_tables()[serial].add_entry(*this,result);
 970 }
 971
 972 // public
 973
 974 unsigned function::register_new(function_options const & opt)
 975 {
 976         unsigned same_name = 0;
 977         for (unsigned i=0; i<registered_functions().size(); ++i) {
 978                 if (registered_functions()[i].name==opt.name) {
 979                         ++same_name;
 980                 }
 981         }
 982         if (same_name>=opt.functions_with_same_name) {
 983                 // we do not throw an exception here because this code is
 984                 // usually executed before main(), so the exception could not
 985                 // caught anyhow
 986                 std::cerr << "WARNING: function name " << opt.name
 987                                   << " already in use!" << std::endl;
 988         }
 989         registered_functions().push_back(opt);
 990         if (opt.use_remember) {
 991                 remember_table::remember_tables().
 992                         push_back(remember_table(opt.remember_size,
 993                                                                          opt.remember_assoc_size,
 994                                                                          opt.remember_strategy));
 995         } else {
 996                 remember_table::remember_tables().push_back(remember_table());
 997         }
 998         return registered_functions().size()-1;
 999 }
1000
1001 /** Find serial number of function by name and number of parameters.
1002  *  Throws exception if function was not found. */
1003 unsigned function::find_function(const std::string &name, unsigned nparams)
1004 {
1005         std::vector<function_options>::const_iterator i = function::registered_functions().begin(), end = function::registered_functions().end();
1006         unsigned serial = 0;
1007         while (i != end) {
1008                 if (i->get_name() == name && i->get_nparams() == nparams)
1009                         return serial;
1010                 ++i;
1011                 ++serial;
1012         }
1013         throw (std::runtime_error("no function '" + name + "' with " + ToString(nparams) + " parameters defined"));
1014 }
1015
1016 /** Return the print name of the function. */
1017 std::string function::get_name(void) const
1018 {
1019         GINAC_ASSERT(serial<registered_functions().size());
1020         return registered_functions()[serial].name;
1021 }
1022
1023 } // namespace GiNaC
1024
1025 END_OF_IMPLEMENTATION
1026
1027 print "Creating interface file function.h...";
1028 open OUT,">function.h" or die "cannot open function.h";
1029 print OUT $interface;
1030 close OUT;
1031 print "ok.\n";
1032
1033 print "Creating implementation file function.cpp...";
1034 open OUT,">function.cpp" or die "cannot open function.cpp";
1035 print OUT $implementation;
1036 close OUT;
1037 print "ok.\n";
1038
1039 print "done.\n";