ginac/function.pl

   1 $maxargs=13;
   2
   3 sub generate_seq {
   4         my ($seq_template,$n)=@_;
   5         my ($res,$N);
   6
   7         $res='';
   8         for ($N=1; $N<=$n; $N++) {
   9                 $res .= eval('"' . $seq_template . '"');
  10                 if ($N!=$n) {
  11                         $res .= ', ';
  12                 }
  13         }
  14         return $res;
  15 }
  16
  17 sub generate_from_to {
  18         my ($template,$seq_template1,$seq_template2,$seq_template3,$from,$to)=@_;
  19         my ($res,$N,$SEQ);
  20
  21         $res='';
  22         for ($N=$from; $N<=$to; $N++) {
  23                 $SEQ1=generate_seq($seq_template1,$N);
  24                 $SEQ2=generate_seq($seq_template2,$N);
  25                 $SEQ3=generate_seq($seq_template3,$N);
  26                 $res .= eval('"' . $template . '"');
  27                 $SEQ1=''; # to avoid main::SEQ1 used only once warning
  28                 $SEQ2=''; # same as above
  29                 $SEQ3=''; # same as above
  30         }
  31         return $res;
  32 }
  33
  34 sub generate {
  35         my ($template,$seq_template1,$seq_template2,$seq_template3)=@_;
  36         return generate_from_to($template,$seq_template1,$seq_template2,$seq_template3,1,$maxargs);
  37 }
  38
  39 $declare_function_macro = generate(
  40         <<'END_OF_DECLARE_FUNCTION_MACRO','typename T${N}','const T${N} & p${N}','GiNaC::ex(p${N})');
  41 #define DECLARE_FUNCTION_${N}P(NAME) \\
  42 extern const unsigned function_index_##NAME; \\
  43 template<${SEQ1}> \\
  44 inline const GiNaC::function NAME(${SEQ2}) { \\
  45         return GiNaC::function(function_index_##NAME, ${SEQ3}); \\
  46 }
  47
  48 END_OF_DECLARE_FUNCTION_MACRO
  49
  50 $typedef_eval_funcp=generate(
  51 'typedef ex (* eval_funcp_${N})(${SEQ1});'."\n",
  52 'const ex &','','');
  53
  54 $typedef_evalf_funcp=generate(
  55 'typedef ex (* evalf_funcp_${N})(${SEQ1});'."\n",
  56 'const ex &','','');
  57
  58 $typedef_derivative_funcp=generate(
  59 'typedef ex (* derivative_funcp_${N})(${SEQ1}, unsigned);'."\n",
  60 'const ex &','','');
  61
  62 $typedef_series_funcp=generate(
  63 'typedef ex (* series_funcp_${N})(${SEQ1}, const relational &, int, unsigned);'."\n",
  64 'const ex &','','');
  65
  66 $eval_func_interface=generate('    function_options & eval_func(eval_funcp_${N} e);'."\n",'','','');
  67
  68 $evalf_func_interface=generate('    function_options & evalf_func(evalf_funcp_${N} ef);'."\n",'','','');
  69
  70 $derivative_func_interface=generate('    function_options & derivative_func(derivative_funcp_${N} d);'."\n",'','','');
  71
  72 $series_func_interface=generate('    function_options & series_func(series_funcp_${N} s);'."\n",'','','');
  73
  74 $constructors_interface=generate(
  75 '    function(unsigned ser, ${SEQ1});'."\n",
  76 'const ex & param${N}','','');
  77
  78 $constructors_implementation=generate(
  79         <<'END_OF_CONSTRUCTORS_IMPLEMENTATION','const ex & param${N}','param${N}','');
  80 function::function(unsigned ser, ${SEQ1})
  81         : exprseq(${SEQ2}), serial(ser)
  82 {
  83         debugmsg(\"function ctor from unsigned,${N}*ex\",LOGLEVEL_CONSTRUCT);
  84         tinfo_key = TINFO_function;
  85 }
  86 END_OF_CONSTRUCTORS_IMPLEMENTATION
  87
  88 $eval_switch_statement=generate(
  89         <<'END_OF_EVAL_SWITCH_STATEMENT','seq[${N}-1]','','');
  90         case ${N}:
  91                 eval_result = ((eval_funcp_${N})(registered_functions()[serial].eval_f))(${SEQ1});
  92                 break;
  93 END_OF_EVAL_SWITCH_STATEMENT
  94
  95 $evalf_switch_statement=generate(
  96         <<'END_OF_EVALF_SWITCH_STATEMENT','eseq[${N}-1]','','');
  97         case ${N}:
  98                 return ((evalf_funcp_${N})(registered_functions()[serial].evalf_f))(${SEQ1});
  99 END_OF_EVALF_SWITCH_STATEMENT
 100
 101 $diff_switch_statement=generate(
 102         <<'END_OF_DIFF_SWITCH_STATEMENT','seq[${N}-1]','','');
 103         case ${N}:
 104                 return ((derivative_funcp_${N})(registered_functions()[serial].derivative_f))(${SEQ1},diff_param);
 105 END_OF_DIFF_SWITCH_STATEMENT
 106
 107 $series_switch_statement=generate(
 108         <<'END_OF_SERIES_SWITCH_STATEMENT','seq[${N}-1]','','');
 109         case ${N}:
 110                 try {
 111                         res = ((series_funcp_${N})(registered_functions()[serial].series_f))(${SEQ1},r,order,options);
 112                 } catch (do_taylor) {
 113                         res = basic::series(r, order, options);
 114                 }
 115                 return res;
 116 END_OF_SERIES_SWITCH_STATEMENT
 117
 118 $eval_func_implementation=generate(
 119         <<'END_OF_EVAL_FUNC_IMPLEMENTATION','','','');
 120 function_options & function_options::eval_func(eval_funcp_${N} e)
 121 {
 122         test_and_set_nparams(${N});
 123         eval_f = eval_funcp(e);
 124         return *this;
 125 }
 126 END_OF_EVAL_FUNC_IMPLEMENTATION
 127
 128 $evalf_func_implementation=generate(
 129         <<'END_OF_EVALF_FUNC_IMPLEMENTATION','','','');
 130 function_options & function_options::evalf_func(evalf_funcp_${N} ef)
 131 {
 132         test_and_set_nparams(${N});
 133         evalf_f = evalf_funcp(ef);
 134         return *this;
 135 }
 136 END_OF_EVALF_FUNC_IMPLEMENTATION
 137
 138 $derivative_func_implementation=generate(
 139         <<'END_OF_DERIVATIVE_FUNC_IMPLEMENTATION','','','');
 140 function_options & function_options::derivative_func(derivative_funcp_${N} d)
 141 {
 142         test_and_set_nparams(${N});
 143         derivative_f = derivative_funcp(d);
 144         return *this;
 145 }
 146 END_OF_DERIVATIVE_FUNC_IMPLEMENTATION
 147
 148 $series_func_implementation=generate(
 149         <<'END_OF_SERIES_FUNC_IMPLEMENTATION','','','');
 150 function_options & function_options::series_func(series_funcp_${N} s)
 151 {
 152         test_and_set_nparams(${N});
 153         series_f = series_funcp(s);
 154         return *this;
 155 }
 156 END_OF_SERIES_FUNC_IMPLEMENTATION
 157
 158 $interface=<<END_OF_INTERFACE;
 159 /** \@file function.h
 160  *
 161  *  Interface to abstract class function (new function concept). */
 162
 163 /*
 164  *  This file was generated automatically by function.pl.
 165  *  Please do not modify it directly, edit the perl script instead!
 166  *  function.pl options: \$maxargs=${maxargs}
 167  *
 168  *  GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
 169  *
 170  *  This program is free software; you can redistribute it and/or modify
 171  *  it under the terms of the GNU General Public License as published by
 172  *  the Free Software Foundation; either version 2 of the License, or
 173  *  (at your option) any later version.
 174  *
 175  *  This program is distributed in the hope that it will be useful,
 176  *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 177  *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 178  *  GNU General Public License for more details.
 179  *
 180  *  You should have received a copy of the GNU General Public License
 181  *  along with this program; if not, write to the Free Software
 182  *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 183  */
 184
 185 #ifndef __GINAC_FUNCTION_H__
 186 #define __GINAC_FUNCTION_H__
 187
 188 #include <string>
 189 #include <vector>
 190
 191 // CINT needs <algorithm> to work properly with <vector>
 192 #include <algorithm>
 193
 194 #include "exprseq.h"
 195
 196 // the following lines have been generated for max. ${maxargs} parameters
 197 $declare_function_macro
 198 // end of generated lines
 199
 200 #define REGISTER_FUNCTION(NAME,OPT) \\
 201 const unsigned function_index_##NAME= \\
 202         GiNaC::function::register_new(GiNaC::function_options(#NAME).OPT);
 203
 204 #define BEGIN_TYPECHECK \\
 205 bool automatic_typecheck=true;
 206
 207 #define TYPECHECK(VAR,TYPE) \\
 208 if (!is_exactly_a<TYPE>(VAR)) { \\
 209         automatic_typecheck=false; \\
 210 } else
 211
 212 #define TYPECHECK_INTEGER(VAR) \\
 213 if (!(VAR).info(GiNaC::info_flags::integer)) { \\
 214         automatic_typecheck=false; \\
 215 } else
 216
 217 #define END_TYPECHECK(RV) \\
 218 {} \\
 219 if (!automatic_typecheck) { \\
 220         return RV.hold(); \\
 221 }
 222
 223 namespace GiNaC {
 224
 225 class function;
 226 class symmetry;
 227
 228 typedef ex (* eval_funcp)();
 229 typedef ex (* evalf_funcp)();
 230 typedef ex (* derivative_funcp)();
 231 typedef ex (* series_funcp)();
 232
 233 // the following lines have been generated for max. ${maxargs} parameters
 234 $typedef_eval_funcp
 235 $typedef_evalf_funcp
 236 $typedef_derivative_funcp
 237 $typedef_series_funcp
 238 // end of generated lines
 239
 240 class function_options
 241 {
 242         friend class function;
 243 public:
 244         function_options();
 245         function_options(std::string const & n, std::string const & tn=std::string());
 246         ~function_options();
 247         void initialize(void);
 248         function_options & set_name(std::string const & n, std::string const & tn=std::string());
 249         function_options & latex_name(std::string const & tn);
 250 // the following lines have been generated for max. ${maxargs} parameters
 251 $eval_func_interface
 252 $evalf_func_interface
 253 $derivative_func_interface
 254 $series_func_interface
 255 // end of generated lines
 256         function_options & set_return_type(unsigned rt, unsigned rtt=0);
 257         function_options & do_not_evalf_params(void);
 258         function_options & remember(unsigned size, unsigned assoc_size=0,
 259                                     unsigned strategy=remember_strategies::delete_never);
 260         function_options & overloaded(unsigned o);
 261         function_options & set_symmetry(const symmetry & s);
 262         void test_and_set_nparams(unsigned n);
 263         std::string get_name(void) const { return name; }
 264         unsigned get_nparams(void) const { return nparams; }
 265         bool has_derivative(void) const { return derivative_f != NULL; }
 266
 267 protected:
 268         std::string name;
 269         std::string TeX_name;
 270
 271         unsigned nparams;
 272
 273         eval_funcp eval_f;
 274         evalf_funcp evalf_f;
 275         derivative_funcp derivative_f;
 276         series_funcp series_f;
 277
 278         bool evalf_params_first;
 279
 280         bool use_return_type;
 281         unsigned return_type;
 282         unsigned return_type_tinfo;
 283
 284         bool use_remember;
 285         unsigned remember_size;
 286         unsigned remember_assoc_size;
 287         unsigned remember_strategy;
 288
 289         unsigned functions_with_same_name;
 290
 291         ex symtree;
 292 };
 293
 294 /** The class function is used to implement builtin functions like sin, cos...
 295         and user defined functions */
 296 class function : public exprseq
 297 {
 298         GINAC_DECLARE_REGISTERED_CLASS(function, exprseq)
 299
 300         // CINT has a linking problem
 301 #ifndef __MAKECINT__
 302         friend void ginsh_get_ginac_functions(void);
 303 #endif // def __MAKECINT__
 304
 305         friend class remember_table_entry;
 306         // friend class remember_table_list;
 307         // friend class remember_table;
 308         friend ex Derivative_eval(const ex &, const ex &);
 309
 310 // member functions
 311
 312         // other ctors
 313 public:
 314         function(unsigned ser);
 315         // the following lines have been generated for max. ${maxargs} parameters
 316 $constructors_interface
 317         // end of generated lines
 318         function(unsigned ser, const exprseq & es);
 319         function(unsigned ser, const exvector & v, bool discardable = false);
 320         function(unsigned ser, exvector * vp); // vp will be deleted
 321
 322         // functions overriding virtual functions from bases classes
 323 public:
 324         void print(const print_context & c, unsigned level = 0) const;
 325         unsigned precedence(void) const {return 70;}
 326         int degree(const ex & s) const;
 327         int ldegree(const ex & s) const;
 328         ex coeff(const ex & s, int n = 1) const;
 329         ex expand(unsigned options=0) const;
 330         ex eval(int level=0) const;
 331         ex evalf(int level=0) const;
 332         unsigned calchash(void) const;
 333         ex series(const relational & r, int order, unsigned options = 0) const;
 334         ex thisexprseq(const exvector & v) const;
 335         ex thisexprseq(exvector * vp) const;
 336 protected:
 337         ex derivative(const symbol & s) const;
 338         bool is_equal_same_type(const basic & other) const;
 339         bool match_same_type(const basic & other) const;
 340         unsigned return_type(void) const;
 341         unsigned return_type_tinfo(void) const;
 342
 343         // new virtual functions which can be overridden by derived classes
 344         // none
 345
 346         // non-virtual functions in this class
 347 protected:
 348         ex pderivative(unsigned diff_param) const; // partial differentiation
 349         static std::vector<function_options> & registered_functions(void);
 350         bool lookup_remember_table(ex & result) const;
 351         void store_remember_table(ex const & result) const;
 352 public:
 353         static unsigned register_new(function_options const & opt);
 354         static unsigned find_function(const std::string &name, unsigned nparams);
 355         unsigned get_serial(void) const {return serial;}
 356         std::string get_name(void) const;
 357
 358 // member variables
 359
 360 protected:
 361         unsigned serial;
 362 };
 363
 364 // utility functions/macros
 365 /** Return the object of type function handled by an ex.
 366  *  This is unsafe: you need to check the type first. */
 367 inline const function &ex_to_function(const ex &e)
 368 {
 369         return static_cast<const function &>(*e.bp);
 370 }
 371
 372 /** Specialization of is_exactly_a<function>(obj) for objects of type function. */
 373 template<> inline bool is_exactly_a<function>(const basic & obj)
 374 {
 375         return obj.tinfo()==TINFO_function;
 376 }
 377
 378 #define is_ex_the_function(OBJ, FUNCNAME) \\
 379         (is_ex_exactly_of_type(OBJ, function) && static_cast<GiNaC::function *>(OBJ.bp)->get_serial() == function_index_##FUNCNAME)
 380
 381 } // namespace GiNaC
 382
 383 #endif // ndef __GINAC_FUNCTION_H__
 384
 385 END_OF_INTERFACE
 386
 387 $implementation=<<END_OF_IMPLEMENTATION;
 388 /** \@file function.cpp
 389  *
 390  *  Implementation of class function. */
 391
 392 /*
 393  *  This file was generated automatically by function.pl.
 394  *  Please do not modify it directly, edit the perl script instead!
 395  *  function.pl options: \$maxargs=${maxargs}
 396  *
 397  *  GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
 398  *
 399  *  This program is free software; you can redistribute it and/or modify
 400  *  it under the terms of the GNU General Public License as published by
 401  *  the Free Software Foundation; either version 2 of the License, or
 402  *  (at your option) any later version.
 403  *
 404  *  This program is distributed in the hope that it will be useful,
 405  *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 406  *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 407  *  GNU General Public License for more details.
 408  *
 409  *  You should have received a copy of the GNU General Public License
 410  *  along with this program; if not, write to the Free Software
 411  *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 412  */
 413
 414 #include <string>
 415 #include <stdexcept>
 416 #include <list>
 417
 418 #include "function.h"
 419 #include "ex.h"
 420 #include "lst.h"
 421 #include "symmetry.h"
 422 #include "print.h"
 423 #include "archive.h"
 424 #include "inifcns.h"
 425 #include "utils.h"
 426 #include "debugmsg.h"
 427 #include "remember.h"
 428
 429 namespace GiNaC {
 430
 431 //////////
 432 // helper class function_options
 433 //////////
 434
 435 function_options::function_options()
 436 {
 437         initialize();
 438 }
 439
 440 function_options::function_options(std::string const & n, std::string const & tn)
 441 {
 442         initialize();
 443         set_name(n,tn);
 444 }
 445
 446 function_options::~function_options()
 447 {
 448         // nothing to clean up at the moment
 449 }
 450
 451 void function_options::initialize(void)
 452 {
 453         set_name("unnamed_function","\\\\mbox{unnamed}");
 454         nparams = 0;
 455         eval_f = evalf_f = derivative_f = series_f = 0;
 456         evalf_params_first = true;
 457         use_return_type = false;
 458         use_remember = false;
 459         functions_with_same_name = 1;
 460         symtree = 0;
 461 }
 462
 463 function_options & function_options::set_name(std::string const & n,
 464                                               std::string const & tn)
 465 {
 466         name=n;
 467         if (tn==std::string())
 468                 TeX_name = "\\\\mbox{"+name+"}";
 469         else
 470                 TeX_name = tn;
 471         return *this;
 472 }
 473
 474 function_options & function_options::latex_name(std::string const & tn)
 475 {
 476         TeX_name=tn;
 477         return *this;
 478 }
 479
 480 // the following lines have been generated for max. ${maxargs} parameters
 481 $eval_func_implementation
 482 $evalf_func_implementation
 483 $derivative_func_implementation
 484 $series_func_implementation
 485 // end of generated lines
 486
 487 function_options & function_options::set_return_type(unsigned rt, unsigned rtt)
 488 {
 489         use_return_type = true;
 490         return_type = rt;
 491         return_type_tinfo = rtt;
 492         return *this;
 493 }
 494
 495 function_options & function_options::do_not_evalf_params(void)
 496 {
 497         evalf_params_first = false;
 498         return *this;
 499 }
 500
 501 function_options & function_options::remember(unsigned size,
 502                                               unsigned assoc_size,
 503                                               unsigned strategy)
 504 {
 505         use_remember = true;
 506         remember_size = size;
 507         remember_assoc_size = assoc_size;
 508         remember_strategy = strategy;
 509         return *this;
 510 }
 511
 512 function_options & function_options::overloaded(unsigned o)
 513 {
 514         functions_with_same_name = o;
 515         return *this;
 516 }
 517
 518 function_options & function_options::set_symmetry(const symmetry & s)
 519 {
 520         symtree = s;
 521         return *this;
 522 }
 523
 524 void function_options::test_and_set_nparams(unsigned n)
 525 {
 526         if (nparams==0) {
 527                 nparams = n;
 528         } else if (nparams!=n) {
 529                 // we do not throw an exception here because this code is
 530                 // usually executed before main(), so the exception could not
 531                 // caught anyhow
 532                 std::cerr << "WARNING: number of parameters ("
 533                           << n << ") differs from number set before ("
 534                           << nparams << ")" << std::endl;
 535         }
 536 }
 537
 538 GINAC_IMPLEMENT_REGISTERED_CLASS(function, exprseq)
 539
 540 //////////
 541 // default ctor, dtor, copy ctor assignment operator and helpers
 542 //////////
 543
 544 // public
 545
 546 function::function() : serial(0)
 547 {
 548         debugmsg("function default ctor",LOGLEVEL_CONSTRUCT);
 549         tinfo_key = TINFO_function;
 550 }
 551
 552 // protected
 553
 554 void function::copy(const function & other)
 555 {
 556         inherited::copy(other);
 557         serial = other.serial;
 558 }
 559
 560 void function::destroy(bool call_parent)
 561 {
 562         if (call_parent)
 563                 inherited::destroy(call_parent);
 564 }
 565
 566 //////////
 567 // other ctors
 568 //////////
 569
 570 // public
 571
 572 function::function(unsigned ser) : serial(ser)
 573 {
 574         debugmsg("function ctor from unsigned",LOGLEVEL_CONSTRUCT);
 575         tinfo_key = TINFO_function;
 576 }
 577
 578 // the following lines have been generated for max. ${maxargs} parameters
 579 $constructors_implementation
 580 // end of generated lines
 581
 582 function::function(unsigned ser, const exprseq & es) : exprseq(es), serial(ser)
 583 {
 584         debugmsg("function ctor from unsigned,exprseq",LOGLEVEL_CONSTRUCT);
 585         tinfo_key = TINFO_function;
 586 }
 587
 588 function::function(unsigned ser, const exvector & v, bool discardable)
 589   : exprseq(v,discardable), serial(ser)
 590 {
 591         debugmsg("function ctor from string,exvector,bool",LOGLEVEL_CONSTRUCT);
 592         tinfo_key = TINFO_function;
 593 }
 594
 595 function::function(unsigned ser, exvector * vp)
 596   : exprseq(vp), serial(ser)
 597 {
 598         debugmsg("function ctor from unsigned,exvector *",LOGLEVEL_CONSTRUCT);
 599         tinfo_key = TINFO_function;
 600 }
 601
 602 //////////
 603 // archiving
 604 //////////
 605
 606 /** Construct object from archive_node. */
 607 function::function(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
 608 {
 609         debugmsg("function ctor from archive_node", LOGLEVEL_CONSTRUCT);
 610
 611         // Find serial number by function name
 612         std::string s;
 613         if (n.find_string("name", s)) {
 614                 unsigned int ser = 0;
 615                 std::vector<function_options>::const_iterator i = registered_functions().begin(), iend = registered_functions().end();
 616                 while (i != iend) {
 617                         if (s == i->name) {
 618                                 serial = ser;
 619                                 return;
 620                         }
 621                         ++i; ++ser;
 622                 }
 623                 throw (std::runtime_error("unknown function '" + s + "' in archive"));
 624         } else
 625                 throw (std::runtime_error("unnamed function in archive"));
 626 }
 627
 628 /** Unarchive the object. */
 629 ex function::unarchive(const archive_node &n, const lst &sym_lst)
 630 {
 631         return (new function(n, sym_lst))->setflag(status_flags::dynallocated);
 632 }
 633
 634 /** Archive the object. */
 635 void function::archive(archive_node &n) const
 636 {
 637         inherited::archive(n);
 638         GINAC_ASSERT(serial < registered_functions().size());
 639         n.add_string("name", registered_functions()[serial].name);
 640 }
 641
 642 //////////
 643 // functions overriding virtual functions from bases classes
 644 //////////
 645
 646 // public
 647
 648 void function::print(const print_context & c, unsigned level) const
 649 {
 650         debugmsg("function print", LOGLEVEL_PRINT);
 651
 652         GINAC_ASSERT(serial<registered_functions().size());
 653
 654         if (is_of_type(c, print_tree)) {
 655
 656                 c.s << std::string(level, ' ') << class_name() << " "
 657                     << registered_functions()[serial].name
 658                     << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
 659                     << ", nops=" << nops()
 660                     << std::endl;
 661                 unsigned delta_indent = static_cast<const print_tree &>(c).delta_indent;
 662                 for (unsigned i=0; i<seq.size(); ++i)
 663                         seq[i].print(c, level + delta_indent);
 664                 c.s << std::string(level + delta_indent, ' ') << "=====" << std::endl;
 665
 666         } else if (is_of_type(c, print_csrc)) {
 667
 668                 // Print function name in lowercase
 669                 std::string lname = registered_functions()[serial].name;
 670                 unsigned num = lname.size();
 671                 for (unsigned i=0; i<num; i++)
 672                         lname[i] = tolower(lname[i]);
 673                 c.s << lname << "(";
 674
 675                 // Print arguments, separated by commas
 676                 exvector::const_iterator it = seq.begin(), itend = seq.end();
 677                 while (it != itend) {
 678                         it->print(c);
 679                         ++it;
 680                         if (it != itend)
 681                                 c.s << ",";
 682                 }
 683                 c.s << ")";
 684
 685         } else if (is_of_type(c, print_latex)) {
 686                 c.s << registered_functions()[serial].TeX_name;
 687                 printseq(c, '(', ',', ')', exprseq::precedence(), function::precedence());
 688         } else {
 689                 c.s << registered_functions()[serial].name;
 690                 printseq(c, '(', ',', ')', exprseq::precedence(), function::precedence());
 691         }
 692 }
 693
 694 ex function::expand(unsigned options) const
 695 {
 696         // Only expand arguments when asked to do so
 697         if (options & expand_options::expand_function_args)
 698                 return inherited::expand(options);
 699         else
 700                 return (options == 0) ? setflag(status_flags::expanded) : *this;
 701 }
 702
 703 int function::degree(const ex & s) const
 704 {
 705         return is_equal(*s.bp) ? 1 : 0;
 706 }
 707
 708 int function::ldegree(const ex & s) const
 709 {
 710         return is_equal(*s.bp) ? 1 : 0;
 711 }
 712
 713 ex function::coeff(const ex & s, int n) const
 714 {
 715         if (is_equal(*s.bp))
 716                 return n==1 ? _ex1() : _ex0();
 717         else
 718                 return n==0 ? ex(*this) : _ex0();
 719 }
 720
 721 ex function::eval(int level) const
 722 {
 723         GINAC_ASSERT(serial<registered_functions().size());
 724
 725         if (level>1) {
 726                 // first evaluate children, then we will end up here again
 727                 return function(serial,evalchildren(level));
 728         }
 729
 730         const function_options &opt = registered_functions()[serial];
 731
 732         // Canonicalize argument order according to the symmetry properties
 733         if (seq.size() > 1 && !(opt.symtree.is_zero())) {
 734                 exvector v = seq;
 735                 GINAC_ASSERT(is_ex_exactly_of_type(opt.symtree, symmetry));
 736                 int sig = canonicalize(v.begin(), ex_to<symmetry>(opt.symtree));
 737                 if (sig != INT_MAX) {
 738                         // Something has changed while sorting arguments, more evaluations later
 739                         if (sig == 0)
 740                                 return _ex0();
 741                         return ex(sig) * thisexprseq(v);
 742                 }
 743         }
 744
 745         if (opt.eval_f==0) {
 746                 return this->hold();
 747         }
 748
 749         bool use_remember = opt.use_remember;
 750         ex eval_result;
 751         if (use_remember && lookup_remember_table(eval_result)) {
 752                 return eval_result;
 753         }
 754
 755         switch (opt.nparams) {
 756                 // the following lines have been generated for max. ${maxargs} parameters
 757 ${eval_switch_statement}
 758                 // end of generated lines
 759         default:
 760                 throw(std::logic_error("function::eval(): invalid nparams"));
 761         }
 762         if (use_remember) {
 763                 store_remember_table(eval_result);
 764         }
 765         return eval_result;
 766 }
 767
 768 ex function::evalf(int level) const
 769 {
 770         GINAC_ASSERT(serial<registered_functions().size());
 771
 772         // Evaluate children first
 773         exvector eseq;
 774         if (level == 1)
 775                 eseq = seq;
 776         else if (level == -max_recursion_level)
 777                 throw(std::runtime_error("max recursion level reached"));
 778         else
 779                 eseq.reserve(seq.size());
 780         --level;
 781         exvector::const_iterator it = seq.begin(), itend = seq.end();
 782         while (it != itend) {
 783                 eseq.push_back(it->evalf(level));
 784                 ++it;
 785         }
 786
 787         if (registered_functions()[serial].evalf_f==0) {
 788                 return function(serial,eseq).hold();
 789         }
 790         switch (registered_functions()[serial].nparams) {
 791                 // the following lines have been generated for max. ${maxargs} parameters
 792 ${evalf_switch_statement}
 793                 // end of generated lines
 794         }
 795         throw(std::logic_error("function::evalf(): invalid nparams"));
 796 }
 797
 798 unsigned function::calchash(void) const
 799 {
 800         unsigned v = golden_ratio_hash(golden_ratio_hash(tinfo()) ^ serial);
 801         for (unsigned i=0; i<nops(); i++) {
 802                 v = rotate_left_31(v);
 803                 v ^= this->op(i).gethash();
 804         }
 805         v &= 0x7FFFFFFFU;
 806         if (flags & status_flags::evaluated) {
 807                 setflag(status_flags::hash_calculated);
 808                 hashvalue = v;
 809         }
 810         return v;
 811 }
 812
 813 ex function::thisexprseq(const exvector & v) const
 814 {
 815         return function(serial,v);
 816 }
 817
 818 ex function::thisexprseq(exvector * vp) const
 819 {
 820         return function(serial,vp);
 821 }
 822
 823 /** Implementation of ex::series for functions.
 824  *  \@see ex::series */
 825 ex function::series(const relational & r, int order, unsigned options) const
 826 {
 827         GINAC_ASSERT(serial<registered_functions().size());
 828
 829         if (registered_functions()[serial].series_f==0) {
 830                 return basic::series(r, order);
 831         }
 832         ex res;
 833         switch (registered_functions()[serial].nparams) {
 834                 // the following lines have been generated for max. ${maxargs} parameters
 835 ${series_switch_statement}
 836                 // end of generated lines
 837         }
 838         throw(std::logic_error("function::series(): invalid nparams"));
 839 }
 840
 841 // protected
 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                 unsigned num = seq.size();
 872                 for (unsigned i=0; i<num; i++) {
 873                         arg_diff = seq[i].diff(s);
 874                         // We apply the chain rule only when it makes sense.  This is not
 875                         // just for performance reasons but also to allow functions to
 876                         // throw when differentiated with respect to one of its arguments
 877                         // without running into trouble with our automatic full
 878                         // differentiation:
 879                         if (!arg_diff.is_zero())
 880                                 result += pderivative(i)*arg_diff;
 881                 }
 882         }
 883         return result;
 884 }
 885
 886 int function::compare_same_type(const basic & other) const
 887 {
 888         GINAC_ASSERT(is_of_type(other, function));
 889         const function & o = static_cast<const function &>(other);
 890
 891         if (serial != o.serial)
 892                 return serial < o.serial ? -1 : 1;
 893         else
 894                 return exprseq::compare_same_type(o);
 895 }
 896
 897 bool function::is_equal_same_type(const basic & other) const
 898 {
 899         GINAC_ASSERT(is_of_type(other, function));
 900         const function & o = static_cast<const function &>(other);
 901
 902         if (serial != o.serial)
 903                 return false;
 904         else
 905                 return exprseq::is_equal_same_type(o);
 906 }
 907
 908 bool function::match_same_type(const basic & other) const
 909 {
 910         GINAC_ASSERT(is_of_type(other, function));
 911         const function & o = static_cast<const function &>(other);
 912
 913         return serial == o.serial;
 914 }
 915
 916 unsigned function::return_type(void) const
 917 {
 918         if (seq.empty())
 919                 return return_types::commutative;
 920         else
 921                 return seq.begin()->return_type();
 922 }
 923
 924 unsigned function::return_type_tinfo(void) const
 925 {
 926         if (seq.empty())
 927                 return tinfo_key;
 928         else
 929                 return seq.begin()->return_type_tinfo();
 930 }
 931
 932 //////////
 933 // new virtual functions which can be overridden by derived classes
 934 //////////
 935
 936 // none
 937
 938 //////////
 939 // non-virtual functions in this class
 940 //////////
 941
 942 // protected
 943
 944 ex function::pderivative(unsigned diff_param) const // partial differentiation
 945 {
 946         GINAC_ASSERT(serial<registered_functions().size());
 947
 948         if (registered_functions()[serial].derivative_f==0) {
 949                 return Derivative(*this, lst(ex(diff_param)));
 950         }
 951         switch (registered_functions()[serial].nparams) {
 952                 // the following lines have been generated for max. ${maxargs} parameters
 953 ${diff_switch_statement}
 954                 // end of generated lines
 955         }
 956         throw(std::logic_error("function::pderivative(): no diff function defined"));
 957 }
 958
 959 std::vector<function_options> & function::registered_functions(void)
 960 {
 961         static std::vector<function_options> * rf = new std::vector<function_options>;
 962         return *rf;
 963 }
 964
 965 bool function::lookup_remember_table(ex & result) const
 966 {
 967         return remember_table::remember_tables()[serial].lookup_entry(*this,result);
 968 }
 969
 970 void function::store_remember_table(ex const & result) const
 971 {
 972         remember_table::remember_tables()[serial].add_entry(*this,result);
 973 }
 974
 975 // public
 976
 977 unsigned function::register_new(function_options const & opt)
 978 {
 979         unsigned same_name = 0;
 980         for (unsigned i=0; i<registered_functions().size(); ++i) {
 981                 if (registered_functions()[i].name==opt.name) {
 982                         ++same_name;
 983                 }
 984         }
 985         if (same_name>=opt.functions_with_same_name) {
 986                 // we do not throw an exception here because this code is
 987                 // usually executed before main(), so the exception could not
 988                 // caught anyhow
 989                 std::cerr << "WARNING: function name " << opt.name
 990                           << " already in use!" << std::endl;
 991         }
 992         registered_functions().push_back(opt);
 993         if (opt.use_remember) {
 994                 remember_table::remember_tables().
 995                         push_back(remember_table(opt.remember_size,
 996                                                  opt.remember_assoc_size,
 997                                                  opt.remember_strategy));
 998         } else {
 999                 remember_table::remember_tables().push_back(remember_table());
1000         }
1001         return registered_functions().size()-1;
1002 }
1003
1004 /** Find serial number of function by name and number of parameters.
1005  *  Throws exception if function was not found. */
1006 unsigned function::find_function(const std::string &name, unsigned nparams)
1007 {
1008         std::vector<function_options>::const_iterator i = function::registered_functions().begin(), end = function::registered_functions().end();
1009         unsigned serial = 0;
1010         while (i != end) {
1011                 if (i->get_name() == name && i->get_nparams() == nparams)
1012                         return serial;
1013                 ++i;
1014                 ++serial;
1015         }
1016         throw (std::runtime_error("no function '" + name + "' with " + ToString(nparams) + " parameters defined"));
1017 }
1018
1019 /** Return the print name of the function. */
1020 std::string function::get_name(void) const
1021 {
1022         GINAC_ASSERT(serial<registered_functions().size());
1023         return registered_functions()[serial].name;
1024 }
1025
1026 } // namespace GiNaC
1027
1028 END_OF_IMPLEMENTATION
1029
1030 print "Creating interface file function.h...";
1031 open OUT,">function.h" or die "cannot open function.h";
1032 print OUT $interface;
1033 close OUT;
1034 print "ok.\n";
1035
1036 print "Creating implementation file function.cpp...";
1037 open OUT,">function.cpp" or die "cannot open function.cpp";
1038 print OUT $implementation;
1039 close OUT;
1040 print "ok.\n";
1041
1042 print "done.\n";