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 BEGIN_TYPECHECK \\
 216 bool automatic_typecheck=true;
 217
 218 #define TYPECHECK(VAR,TYPE) \\
 219 if (!is_exactly_a<TYPE>(VAR)) { \\
 220         automatic_typecheck=false; \\
 221 } else
 222
 223 #define TYPECHECK_INTEGER(VAR) \\
 224 if (!(VAR).info(GiNaC::info_flags::integer)) { \\
 225         automatic_typecheck=false; \\
 226 } else
 227
 228 #define END_TYPECHECK(RV) \\
 229 {} \\
 230 if (!automatic_typecheck) { \\
 231         return RV.hold(); \\
 232 }
 233
 234 namespace GiNaC {
 235
 236 class function;
 237 class symmetry;
 238
 239 typedef ex (* eval_funcp)();
 240 typedef ex (* evalf_funcp)();
 241 typedef ex (* derivative_funcp)();
 242 typedef ex (* series_funcp)();
 243
 244 // the following lines have been generated for max. ${maxargs} parameters
 245 $typedef_eval_funcp
 246 $typedef_evalf_funcp
 247 $typedef_derivative_funcp
 248 $typedef_series_funcp
 249 // end of generated lines
 250
 251 class function_options
 252 {
 253         friend class function;
 254 public:
 255         function_options();
 256         function_options(std::string const & n, std::string const & tn=std::string());
 257         ~function_options();
 258         void initialize(void);
 259         function_options & set_name(std::string const & n, std::string const & tn=std::string());
 260         function_options & latex_name(std::string const & tn);
 261 // the following lines have been generated for max. ${maxargs} parameters
 262 $eval_func_interface
 263 $evalf_func_interface
 264 $derivative_func_interface
 265 $series_func_interface
 266 // end of generated lines
 267         function_options & set_return_type(unsigned rt, unsigned rtt=0);
 268         function_options & do_not_evalf_params(void);
 269         function_options & remember(unsigned size, unsigned assoc_size=0,
 270                                     unsigned strategy=remember_strategies::delete_never);
 271         function_options & overloaded(unsigned o);
 272         function_options & set_symmetry(const symmetry & s);
 273         void test_and_set_nparams(unsigned n);
 274         std::string get_name(void) const { return name; }
 275         unsigned get_nparams(void) const { return nparams; }
 276
 277 protected:
 278         std::string name;
 279         std::string TeX_name;
 280
 281         unsigned nparams;
 282
 283         eval_funcp eval_f;
 284         evalf_funcp evalf_f;
 285         derivative_funcp derivative_f;
 286         series_funcp series_f;
 287
 288         bool evalf_params_first;
 289
 290         bool use_return_type;
 291         unsigned return_type;
 292         unsigned return_type_tinfo;
 293
 294         bool use_remember;
 295         unsigned remember_size;
 296         unsigned remember_assoc_size;
 297         unsigned remember_strategy;
 298
 299         unsigned functions_with_same_name;
 300
 301         ex symtree;
 302 };
 303
 304 /** The class function is used to implement builtin functions like sin, cos...
 305         and user defined functions */
 306 class function : public exprseq
 307 {
 308         GINAC_DECLARE_REGISTERED_CLASS(function, exprseq)
 309
 310         // CINT has a linking problem
 311 #ifndef __MAKECINT__
 312         friend void ginsh_get_ginac_functions(void);
 313 #endif // def __MAKECINT__
 314
 315         friend class remember_table_entry;
 316         // friend class remember_table_list;
 317         // friend class remember_table;
 318
 319 // member functions
 320
 321         // other ctors
 322 public:
 323         function(unsigned ser);
 324         // the following lines have been generated for max. ${maxargs} parameters
 325 $constructors_interface
 326         // end of generated lines
 327         function(unsigned ser, const exprseq & es);
 328         function(unsigned ser, const exvector & v, bool discardable = false);
 329         function(unsigned ser, exvector * vp); // vp will be deleted
 330
 331         // functions overriding virtual functions from bases classes
 332 public:
 333         void print(const print_context & c, unsigned level = 0) const;
 334         unsigned precedence(void) const {return 70;}
 335         int degree(const ex & s) const;
 336         int ldegree(const ex & s) const;
 337         ex coeff(const ex & s, int n = 1) const;
 338         ex expand(unsigned options=0) const;
 339         ex eval(int level=0) const;
 340         ex evalf(int level=0) const;
 341         unsigned calchash(void) const;
 342         ex series(const relational & r, int order, unsigned options = 0) const;
 343         bool match(const ex & pattern, lst & repl_lst) const;
 344         ex thisexprseq(const exvector & v) const;
 345         ex thisexprseq(exvector * vp) const;
 346 protected:
 347         ex derivative(const symbol & s) const;
 348         bool is_equal_same_type(const basic & other) const;
 349         unsigned return_type(void) const;
 350         unsigned return_type_tinfo(void) const;
 351
 352         // new virtual functions which can be overridden by derived classes
 353         // none
 354
 355         // non-virtual functions in this class
 356 protected:
 357         ex pderivative(unsigned diff_param) const; // partial differentiation
 358         static std::vector<function_options> & registered_functions(void);
 359         bool lookup_remember_table(ex & result) const;
 360         void store_remember_table(ex const & result) const;
 361 public:
 362         static unsigned register_new(function_options const & opt);
 363         static unsigned find_function(const std::string &name, unsigned nparams);
 364         unsigned get_serial(void) const {return serial;}
 365         std::string get_name(void) const;
 366
 367 // member variables
 368
 369 protected:
 370         unsigned serial;
 371 };
 372
 373 // utility functions/macros
 374 /** Return the object of type function handled by an ex.
 375  *  This is unsafe: you need to check the type first. */
 376 inline const function &ex_to_function(const ex &e)
 377 {
 378         return static_cast<const function &>(*e.bp);
 379 }
 380
 381 /** Specialization of is_exactly_a<function>(obj) for objects of type function. */
 382 template<> inline bool is_exactly_a<function>(const basic & obj)
 383 {
 384         return obj.tinfo()==TINFO_function;
 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         return *this;
 481 }
 482
 483 function_options & function_options::latex_name(std::string const & tn)
 484 {
 485         TeX_name=tn;
 486         return *this;
 487 }
 488
 489 // the following lines have been generated for max. ${maxargs} parameters
 490 $eval_func_implementation
 491 $evalf_func_implementation
 492 $derivative_func_implementation
 493 $series_func_implementation
 494 // end of generated lines
 495
 496 function_options & function_options::set_return_type(unsigned rt, unsigned rtt)
 497 {
 498         use_return_type = true;
 499         return_type = rt;
 500         return_type_tinfo = rtt;
 501         return *this;
 502 }
 503
 504 function_options & function_options::do_not_evalf_params(void)
 505 {
 506         evalf_params_first = false;
 507         return *this;
 508 }
 509
 510 function_options & function_options::remember(unsigned size,
 511                                               unsigned assoc_size,
 512                                               unsigned strategy)
 513 {
 514         use_remember = true;
 515         remember_size = size;
 516         remember_assoc_size = assoc_size;
 517         remember_strategy = strategy;
 518         return *this;
 519 }
 520
 521 function_options & function_options::overloaded(unsigned o)
 522 {
 523         functions_with_same_name = o;
 524         return *this;
 525 }
 526
 527 function_options & function_options::set_symmetry(const symmetry & s)
 528 {
 529         symtree = s;
 530         return *this;
 531 }
 532
 533 void function_options::test_and_set_nparams(unsigned n)
 534 {
 535         if (nparams==0) {
 536                 nparams = n;
 537         } else if (nparams!=n) {
 538                 // we do not throw an exception here because this code is
 539                 // usually executed before main(), so the exception could not
 540                 // caught anyhow
 541                 std::cerr << "WARNING: number of parameters ("
 542                           << n << ") differs from number set before ("
 543                           << nparams << ")" << std::endl;
 544         }
 545 }
 546
 547 GINAC_IMPLEMENT_REGISTERED_CLASS(function, exprseq)
 548
 549 //////////
 550 // default ctor, dtor, copy ctor assignment operator and helpers
 551 //////////
 552
 553 // public
 554
 555 function::function() : serial(0)
 556 {
 557         debugmsg("function default ctor",LOGLEVEL_CONSTRUCT);
 558         tinfo_key = TINFO_function;
 559 }
 560
 561 // protected
 562
 563 void function::copy(const function & other)
 564 {
 565         inherited::copy(other);
 566         serial = other.serial;
 567 }
 568
 569 void function::destroy(bool call_parent)
 570 {
 571         if (call_parent)
 572                 inherited::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<seq.size(); ++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                 unsigned num = lname.size();
 680                 for (unsigned i=0; i<num; i++)
 681                         lname[i] = tolower(lname[i]);
 682                 c.s << lname << "(";
 683
 684                 // Print arguments, separated by commas
 685                 exvector::const_iterator it = seq.begin(), itend = seq.end();
 686                 while (it != itend) {
 687                         it->print(c);
 688                         it++;
 689                         if (it != itend)
 690                                 c.s << ",";
 691                 }
 692                 c.s << ")";
 693
 694         } else if (is_of_type(c, print_latex)) {
 695                 c.s << registered_functions()[serial].TeX_name;
 696                 printseq(c, '(', ',', ')', exprseq::precedence(), function::precedence());
 697         } else {
 698                 c.s << registered_functions()[serial].name;
 699                 printseq(c, '(', ',', ')', exprseq::precedence(), function::precedence());
 700         }
 701 }
 702
 703 ex function::expand(unsigned options) const
 704 {
 705         return this->setflag(status_flags::expanded);
 706 }
 707
 708 int function::degree(const ex & s) const
 709 {
 710         return is_equal(*s.bp) ? 1 : 0;
 711 }
 712
 713 int function::ldegree(const ex & s) const
 714 {
 715         return is_equal(*s.bp) ? 1 : 0;
 716 }
 717
 718 ex function::coeff(const ex & s, int n) const
 719 {
 720         if (is_equal(*s.bp))
 721                 return n==1 ? _ex1() : _ex0();
 722         else
 723                 return n==0 ? ex(*this) : _ex0();
 724 }
 725
 726 ex function::eval(int level) const
 727 {
 728         GINAC_ASSERT(serial<registered_functions().size());
 729
 730         if (level>1) {
 731                 // first evaluate children, then we will end up here again
 732                 return function(serial,evalchildren(level));
 733         }
 734
 735         const function_options &opt = registered_functions()[serial];
 736
 737         // Canonicalize argument order according to the symmetry properties
 738         if (seq.size() > 1 && !(opt.symtree.is_zero())) {
 739                 exvector v = seq;
 740                 GINAC_ASSERT(is_ex_exactly_of_type(opt.symtree, symmetry));
 741                 int sig = canonicalize(v.begin(), ex_to<symmetry>(opt.symtree));
 742                 if (sig != INT_MAX) {
 743                         // Something has changed while sorting arguments, more evaluations later
 744                         if (sig == 0)
 745                                 return _ex0();
 746                         return ex(sig) * thisexprseq(v);
 747                 }
 748         }
 749
 750         if (opt.eval_f==0) {
 751                 return this->hold();
 752         }
 753
 754         bool use_remember = opt.use_remember;
 755         ex eval_result;
 756         if (use_remember && lookup_remember_table(eval_result)) {
 757                 return eval_result;
 758         }
 759
 760         switch (opt.nparams) {
 761                 // the following lines have been generated for max. ${maxargs} parameters
 762 ${eval_switch_statement}
 763                 // end of generated lines
 764         default:
 765                 throw(std::logic_error("function::eval(): invalid nparams"));
 766         }
 767         if (use_remember) {
 768                 store_remember_table(eval_result);
 769         }
 770         return eval_result;
 771 }
 772
 773 ex function::evalf(int level) const
 774 {
 775         GINAC_ASSERT(serial<registered_functions().size());
 776
 777         // Evaluate children first
 778         exvector eseq;
 779         if (level == 1)
 780                 eseq = seq;
 781         else if (level == -max_recursion_level)
 782                 throw(std::runtime_error("max recursion level reached"));
 783         else
 784                 eseq.reserve(seq.size());
 785         level--;
 786         exvector::const_iterator it = seq.begin(), itend = seq.end();
 787         while (it != itend) {
 788                 eseq.push_back((*it).evalf(level));
 789                 it++;
 790         }
 791
 792         if (registered_functions()[serial].evalf_f==0) {
 793                 return function(serial,eseq).hold();
 794         }
 795         switch (registered_functions()[serial].nparams) {
 796                 // the following lines have been generated for max. ${maxargs} parameters
 797 ${evalf_switch_statement}
 798                 // end of generated lines
 799         }
 800         throw(std::logic_error("function::evalf(): invalid nparams"));
 801 }
 802
 803 unsigned function::calchash(void) const
 804 {
 805         unsigned v = golden_ratio_hash(golden_ratio_hash(tinfo()) ^ serial);
 806         for (unsigned i=0; i<nops(); i++) {
 807                 v = rotate_left_31(v);
 808                 v ^= this->op(i).gethash();
 809         }
 810         v &= 0x7FFFFFFFU;
 811         if (flags & status_flags::evaluated) {
 812                 setflag(status_flags::hash_calculated);
 813                 hashvalue = v;
 814         }
 815         return v;
 816 }
 817
 818 ex function::thisexprseq(const exvector & v) const
 819 {
 820         return function(serial,v);
 821 }
 822
 823 ex function::thisexprseq(exvector * vp) const
 824 {
 825         return function(serial,vp);
 826 }
 827
 828 /** Implementation of ex::series for functions.
 829  *  \@see ex::series */
 830 ex function::series(const relational & r, int order, unsigned options) const
 831 {
 832         GINAC_ASSERT(serial<registered_functions().size());
 833
 834         if (registered_functions()[serial].series_f==0) {
 835                 return basic::series(r, order);
 836         }
 837         ex res;
 838         switch (registered_functions()[serial].nparams) {
 839                 // the following lines have been generated for max. ${maxargs} parameters
 840 ${series_switch_statement}
 841                 // end of generated lines
 842         }
 843         throw(std::logic_error("function::series(): invalid nparams"));
 844 }
 845
 846 bool function::match(const ex & pattern, lst & repl_lst) const
 847 {
 848         // Serial number must match
 849         if (is_ex_of_type(pattern, function) && serial != ex_to<function>(pattern).serial)
 850                 return false;
 851         return inherited::match(pattern, repl_lst);
 852 }
 853
 854 // protected
 855
 856
 857 /** Implementation of ex::diff() for functions. It applies the chain rule,
 858  *  except for the Order term function.
 859  *  \@see ex::diff */
 860 ex function::derivative(const symbol & s) const
 861 {
 862         ex result;
 863
 864         if (serial == function_index_Order) {
 865                 // Order Term function only differentiates the argument
 866                 return Order(seq[0].diff(s));
 867         } else if (serial == function_index_Derivative) {
 868                 // Inert derivative performs chain rule on the first argument only, and
 869                 // adds differentiation parameter to list (second argument)
 870                 GINAC_ASSERT(is_ex_exactly_of_type(seq[0], function));
 871                 GINAC_ASSERT(is_ex_exactly_of_type(seq[1], function));
 872                 ex fcn = seq[0];
 873                 ex arg_diff;
 874                 for (unsigned i=0; i!=fcn.nops(); i++) {
 875                         arg_diff = fcn.op(i).diff(s);
 876                         if (!arg_diff.is_zero()) {
 877                                 lst new_lst = ex_to<lst>(seq[1]);
 878                                 new_lst.append(i);
 879                                 result += arg_diff * Derivative(fcn, new_lst);
 880                         }
 881                 }
 882         } else {
 883                 // Chain rule
 884                 ex arg_diff;
 885                 unsigned num = seq.size();
 886                 for (unsigned i=0; i<num; i++) {
 887                         arg_diff = seq[i].diff(s);
 888                         // We apply the chain rule only when it makes sense.  This is not
 889                         // just for performance reasons but also to allow functions to
 890                         // throw when differentiated with respect to one of its arguments
 891                         // without running into trouble with our automatic full
 892                         // differentiation:
 893                         if (!arg_diff.is_zero())
 894                                 result += pderivative(i)*arg_diff;
 895                 }
 896         }
 897         return result;
 898 }
 899
 900 int function::compare_same_type(const basic & other) const
 901 {
 902         GINAC_ASSERT(is_of_type(other, function));
 903         const function & o = static_cast<const function &>(other);
 904
 905         if (serial!=o.serial) {
 906                 return serial < o.serial ? -1 : 1;
 907         }
 908         return exprseq::compare_same_type(o);
 909 }
 910
 911 bool function::is_equal_same_type(const basic & other) const
 912 {
 913         GINAC_ASSERT(is_of_type(other, function));
 914         const function & o = static_cast<const function &>(other);
 915
 916         if (serial!=o.serial) return false;
 917         return exprseq::is_equal_same_type(o);
 918 }
 919
 920 unsigned function::return_type(void) const
 921 {
 922         if (seq.empty())
 923                 return return_types::commutative;
 924         else
 925                 return seq.begin()->return_type();
 926 }
 927
 928 unsigned function::return_type_tinfo(void) const
 929 {
 930         if (seq.empty())
 931                 return tinfo_key;
 932         else
 933                 return seq.begin()->return_type_tinfo();
 934 }
 935
 936 //////////
 937 // new virtual functions which can be overridden by derived classes
 938 //////////
 939
 940 // none
 941
 942 //////////
 943 // non-virtual functions in this class
 944 //////////
 945
 946 // protected
 947
 948 ex function::pderivative(unsigned diff_param) const // partial differentiation
 949 {
 950         GINAC_ASSERT(serial<registered_functions().size());
 951
 952         if (registered_functions()[serial].derivative_f==0) {
 953                 return Derivative(*this, lst(ex(diff_param)));
 954         }
 955         switch (registered_functions()[serial].nparams) {
 956                 // the following lines have been generated for max. ${maxargs} parameters
 957 ${diff_switch_statement}
 958                 // end of generated lines
 959         }
 960         throw(std::logic_error("function::pderivative(): no diff function defined"));
 961 }
 962
 963 std::vector<function_options> & function::registered_functions(void)
 964 {
 965         static std::vector<function_options> * rf = new std::vector<function_options>;
 966         return *rf;
 967 }
 968
 969 bool function::lookup_remember_table(ex & result) const
 970 {
 971         return remember_table::remember_tables()[serial].lookup_entry(*this,result);
 972 }
 973
 974 void function::store_remember_table(ex const & result) const
 975 {
 976         remember_table::remember_tables()[serial].add_entry(*this,result);
 977 }
 978
 979 // public
 980
 981 unsigned function::register_new(function_options const & opt)
 982 {
 983         unsigned same_name = 0;
 984         for (unsigned i=0; i<registered_functions().size(); ++i) {
 985                 if (registered_functions()[i].name==opt.name) {
 986                         same_name++;
 987                 }
 988         }
 989         if (same_name>=opt.functions_with_same_name) {
 990                 // we do not throw an exception here because this code is
 991                 // usually executed before main(), so the exception could not
 992                 // caught anyhow
 993                 std::cerr << "WARNING: function name " << opt.name
 994                                   << " already in use!" << std::endl;
 995         }
 996         registered_functions().push_back(opt);
 997         if (opt.use_remember) {
 998                 remember_table::remember_tables().
 999                         push_back(remember_table(opt.remember_size,
1000                                                                          opt.remember_assoc_size,
1001                                                                          opt.remember_strategy));
1002         } else {
1003                 remember_table::remember_tables().push_back(remember_table());
1004         }
1005         return registered_functions().size()-1;
1006 }
1007
1008 /** Find serial number of function by name and number of parameters.
1009  *  Throws exception if function was not found. */
1010 unsigned function::find_function(const std::string &name, unsigned nparams)
1011 {
1012         std::vector<function_options>::const_iterator i = function::registered_functions().begin(), end = function::registered_functions().end();
1013         unsigned serial = 0;
1014         while (i != end) {
1015                 if (i->get_name() == name && i->get_nparams() == nparams)
1016                         return serial;
1017                 i++;
1018                 serial++;
1019         }
1020         throw (std::runtime_error("no function '" + name + "' with " + ToString(nparams) + " parameters defined"));
1021 }
1022
1023 /** Return the print name of the function. */
1024 std::string function::get_name(void) const
1025 {
1026         GINAC_ASSERT(serial<registered_functions().size());
1027         return registered_functions()[serial].name;
1028 }
1029
1030 } // namespace GiNaC
1031
1032 END_OF_IMPLEMENTATION
1033
1034 print "Creating interface file function.h...";
1035 open OUT,">function.h" or die "cannot open function.h";
1036 print OUT $interface;
1037 close OUT;
1038 print "ok.\n";
1039
1040 print "Creating implementation file function.cpp...";
1041 open OUT,">function.cpp" or die "cannot open function.cpp";
1042 print OUT $implementation;
1043 close OUT;
1044 print "ok.\n";
1045
1046 print "done.\n";