ginac/function.pl

   1 $maxargs=13;
   2
   3 sub generate_seq {
   4         my ($seq_template,$n)=@_;
   5         my ($res,$N);
   6
   7         $res='';
   8         for ($N=1; $N<=$n; $N++) {
   9                 $res .= eval('"' . $seq_template . '"');
  10                 if ($N!=$n) {
  11                         $res .= ', ';
  12                 }
  13         }
  14         return $res;
  15 }
  16
  17 sub generate_from_to {
  18         my ($template,$seq_template1,$seq_template2,$from,$to)=@_;
  19         my ($res,$N,$SEQ);
  20
  21         $res='';
  22         for ($N=$from; $N<=$to; $N++) {
  23                 $SEQ1=generate_seq($seq_template1,$N);
  24                 $SEQ2=generate_seq($seq_template2,$N);
  25                 $res .= eval('"' . $template . '"');
  26                 $SEQ1=''; # to avoid main::SEQ1 used only once warning
  27                 $SEQ2=''; # same as above
  28         }
  29         return $res;
  30 }
  31
  32 sub generate {
  33         my ($template,$seq_template1,$seq_template2)=@_;
  34         return generate_from_to($template,$seq_template1,$seq_template2,1,$maxargs);
  35 }
  36
  37 $declare_function_macro = <<'END_OF_DECLARE_FUNCTION_1_AND_2P_MACRO';
  38 #define DECLARE_FUNCTION_1P(NAME) \
  39 extern const unsigned function_index_##NAME; \
  40 inline GiNaC::function NAME(const GiNaC::ex & p1) { \
  41         return GiNaC::function(function_index_##NAME, p1); \
  42 }
  43 #define DECLARE_FUNCTION_2P(NAME) \
  44 extern const unsigned function_index_##NAME; \
  45 inline GiNaC::function NAME(const GiNaC::ex & p1, const GiNaC::ex & p2) { \
  46         return GiNaC::function(function_index_##NAME, p1, p2); \
  47 }
  48
  49 END_OF_DECLARE_FUNCTION_1_AND_2P_MACRO
  50
  51 $declare_function_macro .= generate_from_to(
  52         <<'END_OF_DECLARE_FUNCTION_MACRO','const GiNaC::ex & p${N}','p${N}',3,$maxargs);
  53 #define DECLARE_FUNCTION_${N}P(NAME) \\
  54 extern const unsigned function_index_##NAME; \\
  55 inline GiNaC::function NAME(${SEQ1}) { \\
  56         return GiNaC::function(function_index_##NAME, ${SEQ2}); \\
  57 }
  58
  59 END_OF_DECLARE_FUNCTION_MACRO
  60
  61 $typedef_eval_funcp=generate(
  62 'typedef ex (* eval_funcp_${N})(${SEQ1});'."\n",
  63 'const ex &','');
  64
  65 $typedef_evalf_funcp=generate(
  66 'typedef ex (* evalf_funcp_${N})(${SEQ1});'."\n",
  67 'const ex &','');
  68
  69 $typedef_derivative_funcp=generate(
  70 'typedef ex (* derivative_funcp_${N})(${SEQ1}, unsigned);'."\n",
  71 'const ex &','');
  72
  73 $typedef_series_funcp=generate(
  74 'typedef ex (* series_funcp_${N})(${SEQ1}, const relational &, int, unsigned);'."\n",
  75 'const ex &','');
  76
  77 $eval_func_interface=generate('    function_options & eval_func(eval_funcp_${N} e);'."\n",'','');
  78
  79 $evalf_func_interface=generate('    function_options & evalf_func(evalf_funcp_${N} ef);'."\n",'','');
  80
  81 $derivative_func_interface=generate('    function_options & derivative_func(derivative_funcp_${N} d);'."\n",'','');
  82
  83 $series_func_interface=generate('    function_options & series_func(series_funcp_${N} s);'."\n",'','');
  84
  85 $constructors_interface=generate(
  86 '    function(unsigned ser, ${SEQ1});'."\n",
  87 'const ex & param${N}','');
  88
  89 $constructors_implementation=generate(
  90         <<'END_OF_CONSTRUCTORS_IMPLEMENTATION','const ex & param${N}','param${N}');
  91 function::function(unsigned ser, ${SEQ1})
  92         : exprseq(${SEQ2}), serial(ser)
  93 {
  94         debugmsg(\"function ctor from unsigned,${N}*ex\",LOGLEVEL_CONSTRUCT);
  95         tinfo_key = TINFO_function;
  96 }
  97 END_OF_CONSTRUCTORS_IMPLEMENTATION
  98
  99 $eval_switch_statement=generate(
 100         <<'END_OF_EVAL_SWITCH_STATEMENT','seq[${N}-1]','');
 101         case ${N}:
 102                 eval_result=((eval_funcp_${N})(registered_functions()[serial].eval_f))(${SEQ1});
 103                 break;
 104 END_OF_EVAL_SWITCH_STATEMENT
 105
 106 $evalf_switch_statement=generate(
 107         <<'END_OF_EVALF_SWITCH_STATEMENT','eseq[${N}-1]','');
 108         case ${N}:
 109                 return ((evalf_funcp_${N})(registered_functions()[serial].evalf_f))(${SEQ1});
 110 END_OF_EVALF_SWITCH_STATEMENT
 111
 112 $diff_switch_statement=generate(
 113         <<'END_OF_DIFF_SWITCH_STATEMENT','seq[${N}-1]','');
 114         case ${N}:
 115                 return ((derivative_funcp_${N})(registered_functions()[serial].derivative_f))(${SEQ1},diff_param);
 116 END_OF_DIFF_SWITCH_STATEMENT
 117
 118 $series_switch_statement=generate(
 119         <<'END_OF_SERIES_SWITCH_STATEMENT','seq[${N}-1]','');
 120         case ${N}:
 121                 try {
 122                         res = ((series_funcp_${N})(registered_functions()[serial].series_f))(${SEQ1},r,order,options);
 123                 } catch (do_taylor) {
 124                         res = basic::series(r, order, options);
 125                 }
 126                 return res;
 127 END_OF_SERIES_SWITCH_STATEMENT
 128
 129 $eval_func_implementation=generate(
 130         <<'END_OF_EVAL_FUNC_IMPLEMENTATION','','');
 131 function_options & function_options::eval_func(eval_funcp_${N} e)
 132 {
 133         test_and_set_nparams(${N});
 134         eval_f=eval_funcp(e);
 135         return *this;
 136 }
 137 END_OF_EVAL_FUNC_IMPLEMENTATION
 138
 139 $evalf_func_implementation=generate(
 140         <<'END_OF_EVALF_FUNC_IMPLEMENTATION','','');
 141 function_options & function_options::evalf_func(evalf_funcp_${N} ef)
 142 {
 143         test_and_set_nparams(${N});
 144         evalf_f=evalf_funcp(ef);
 145         return *this;
 146 }
 147 END_OF_EVALF_FUNC_IMPLEMENTATION
 148
 149 $derivative_func_implementation=generate(
 150         <<'END_OF_DERIVATIVE_FUNC_IMPLEMENTATION','','');
 151 function_options & function_options::derivative_func(derivative_funcp_${N} d)
 152 {
 153         test_and_set_nparams(${N});
 154         derivative_f=derivative_funcp(d);
 155         return *this;
 156 }
 157 END_OF_DERIVATIVE_FUNC_IMPLEMENTATION
 158
 159 $series_func_implementation=generate(
 160         <<'END_OF_SERIES_FUNC_IMPLEMENTATION','','');
 161 function_options & function_options::series_func(series_funcp_${N} s)
 162 {
 163         test_and_set_nparams(${N});
 164         series_f=series_funcp(s);
 165         return *this;
 166 }
 167 END_OF_SERIES_FUNC_IMPLEMENTATION
 168
 169 $interface=<<END_OF_INTERFACE;
 170 /** \@file function.h
 171  *
 172  *  Interface to abstract class function (new function concept). */
 173
 174 /*
 175  *  This file was generated automatically by function.pl.
 176  *  Please do not modify it directly, edit the perl script instead!
 177  *  function.pl options: \$maxargs=${maxargs}
 178  *
 179  *  GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
 180  *
 181  *  This program is free software; you can redistribute it and/or modify
 182  *  it under the terms of the GNU General Public License as published by
 183  *  the Free Software Foundation; either version 2 of the License, or
 184  *  (at your option) any later version.
 185  *
 186  *  This program is distributed in the hope that it will be useful,
 187  *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 188  *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 189  *  GNU General Public License for more details.
 190  *
 191  *  You should have received a copy of the GNU General Public License
 192  *  along with this program; if not, write to the Free Software
 193  *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 194  */
 195
 196 #ifndef __GINAC_FUNCTION_H__
 197 #define __GINAC_FUNCTION_H__
 198
 199 #include <string>
 200 #include <vector>
 201
 202 // CINT needs <algorithm> to work properly with <vector>
 203 #include <algorithm>
 204
 205 #include "exprseq.h"
 206
 207 // the following lines have been generated for max. ${maxargs} parameters
 208 $declare_function_macro
 209 // end of generated lines
 210
 211 #define REGISTER_FUNCTION(NAME,OPT) \\
 212 const unsigned function_index_##NAME= \\
 213         GiNaC::function::register_new(GiNaC::function_options(#NAME).OPT);
 214
 215 #define REGISTER_FUNCTION_OLD(NAME,E,EF,D,S) \\
 216 const unsigned function_index_##NAME= \\
 217         GiNaC::function::register_new(GiNaC::function_options(#NAME). \\
 218                                       eval_func(E). \\
 219                                       evalf_func(EF). \\
 220                                       derivative_func(D). \\
 221                                       series_func(S));
 222
 223 #define BEGIN_TYPECHECK \\
 224 bool automatic_typecheck=true;
 225
 226 #define TYPECHECK(VAR,TYPE) \\
 227 if (!is_ex_exactly_of_type(VAR,TYPE)) { \\
 228         automatic_typecheck=false; \\
 229 } else
 230
 231 #define TYPECHECK_INTEGER(VAR) \\
 232 if (!(VAR).info(GiNaC::info_flags::integer)) { \\
 233         automatic_typecheck=false; \\
 234 } else
 235
 236 #define END_TYPECHECK(RV) \\
 237 {} \\
 238 if (!automatic_typecheck) { \\
 239         return RV.hold(); \\
 240 }
 241
 242 namespace GiNaC {
 243
 244 class function;
 245
 246 typedef ex (* eval_funcp)();
 247 typedef ex (* evalf_funcp)();
 248 typedef ex (* derivative_funcp)();
 249 typedef ex (* series_funcp)();
 250
 251 // the following lines have been generated for max. ${maxargs} parameters
 252 $typedef_eval_funcp
 253 $typedef_evalf_funcp
 254 $typedef_derivative_funcp
 255 $typedef_series_funcp
 256 // end of generated lines
 257
 258 class function_options
 259 {
 260         friend class function;
 261 public:
 262         function_options();
 263         function_options(std::string const & n, std::string const & tn=std::string());
 264         ~function_options();
 265         void initialize(void);
 266         function_options & set_name(std::string const & n, std::string const & tn=std::string());
 267 // the following lines have been generated for max. ${maxargs} parameters
 268 $eval_func_interface
 269 $evalf_func_interface
 270 $derivative_func_interface
 271 $series_func_interface
 272 // end of generated lines
 273         function_options & set_return_type(unsigned rt, unsigned rtt=0);
 274         function_options & do_not_evalf_params(void);
 275         function_options & remember(unsigned size, unsigned assoc_size=0,
 276                                     unsigned strategy=remember_strategies::delete_never);
 277         function_options & overloaded(unsigned o);
 278         void test_and_set_nparams(unsigned n);
 279         std::string get_name(void) const { return name; }
 280         unsigned get_nparams(void) const { return nparams; }
 281
 282 protected:
 283         std::string name;
 284         std::string TeX_name;
 285
 286         unsigned nparams;
 287
 288         eval_funcp eval_f;
 289         evalf_funcp evalf_f;
 290         derivative_funcp derivative_f;
 291         series_funcp series_f;
 292
 293         bool evalf_params_first;
 294
 295         bool use_return_type;
 296         unsigned return_type;
 297         unsigned return_type_tinfo;
 298
 299         bool use_remember;
 300         unsigned remember_size;
 301         unsigned remember_assoc_size;
 302         unsigned remember_strategy;
 303
 304         unsigned functions_with_same_name;
 305 };
 306
 307 /** The class function is used to implement builtin functions like sin, cos...
 308         and user defined functions */
 309 class function : public exprseq
 310 {
 311         GINAC_DECLARE_REGISTERED_CLASS(function, exprseq)
 312
 313         // CINT has a linking problem
 314 #ifndef __MAKECINT__
 315         friend void ginsh_get_ginac_functions(void);
 316 #endif // def __MAKECINT__
 317
 318         friend class remember_table_entry;
 319         // friend class remember_table_list;
 320         // friend class remember_table;
 321
 322 // member functions
 323
 324         // other ctors
 325 public:
 326         function(unsigned ser);
 327         // the following lines have been generated for max. ${maxargs} parameters
 328 $constructors_interface
 329         // end of generated lines
 330         function(unsigned ser, const exprseq & es);
 331         function(unsigned ser, const exvector & v, bool discardable=0);
 332         function(unsigned ser, exvector * vp); // vp will be deleted
 333
 334         // functions overriding virtual functions from bases classes
 335 public:
 336         void print(const print_context & c, unsigned level = 0) const;
 337         int degree(const ex & s) const;
 338         int ldegree(const ex & s) const;
 339         ex coeff(const ex & s, int n = 1) const;
 340         ex expand(unsigned options=0) const;
 341         ex eval(int level=0) const;
 342         ex evalf(int level=0) const;
 343         unsigned calchash(void) const;
 344         ex series(const relational & r, int order, unsigned options = 0) const;
 345         ex thisexprseq(const exvector & v) const;
 346         ex thisexprseq(exvector * vp) const;
 347 protected:
 348         ex derivative(const symbol & s) const;
 349         bool is_equal_same_type(const basic & other) const;
 350         unsigned return_type(void) const;
 351         unsigned return_type_tinfo(void) const;
 352
 353         // new virtual functions which can be overridden by derived classes
 354         // none
 355
 356         // non-virtual functions in this class
 357 protected:
 358         ex pderivative(unsigned diff_param) const; // partial differentiation
 359         static std::vector<function_options> & registered_functions(void);
 360         bool lookup_remember_table(ex & result) const;
 361         void store_remember_table(ex const & result) const;
 362 public:
 363         static unsigned register_new(function_options const & opt);
 364         static unsigned find_function(const std::string &name, unsigned nparams);
 365         unsigned getserial(void) const {return serial;}
 366
 367 // member variables
 368
 369 protected:
 370         unsigned serial;
 371 };
 372
 373 // utility functions/macros
 374 inline const function &ex_to_function(const ex &e)
 375 {
 376         return static_cast<const function &>(*e.bp);
 377 }
 378
 379 #define is_ex_the_function(OBJ, FUNCNAME) \\
 380         (is_ex_exactly_of_type(OBJ, function) && static_cast<GiNaC::function *>(OBJ.bp)->getserial() == function_index_##FUNCNAME)
 381
 382 } // namespace GiNaC
 383
 384 #endif // ndef __GINAC_FUNCTION_H__
 385
 386 END_OF_INTERFACE
 387
 388 $implementation=<<END_OF_IMPLEMENTATION;
 389 /** \@file function.cpp
 390  *
 391  *  Implementation of class function. */
 392
 393 /*
 394  *  This file was generated automatically by function.pl.
 395  *  Please do not modify it directly, edit the perl script instead!
 396  *  function.pl options: \$maxargs=${maxargs}
 397  *
 398  *  GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
 399  *
 400  *  This program is free software; you can redistribute it and/or modify
 401  *  it under the terms of the GNU General Public License as published by
 402  *  the Free Software Foundation; either version 2 of the License, or
 403  *  (at your option) any later version.
 404  *
 405  *  This program is distributed in the hope that it will be useful,
 406  *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 407  *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 408  *  GNU General Public License for more details.
 409  *
 410  *  You should have received a copy of the GNU General Public License
 411  *  along with this program; if not, write to the Free Software
 412  *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 413  */
 414
 415 #include <string>
 416 #include <stdexcept>
 417 #include <list>
 418
 419 #include "function.h"
 420 #include "ex.h"
 421 #include "lst.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","\\\\operatorname{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 }
 461
 462 function_options & function_options::set_name(std::string const & n,
 463                                               std::string const & tn)
 464 {
 465         name=n;
 466         if (tn==std::string()) {
 467                 TeX_name="\\\\operatorname{"+name+"}";
 468         } else {
 469                 TeX_name=tn;
 470         }
 471         return *this;
 472 }
 473
 474 // the following lines have been generated for max. ${maxargs} parameters
 475 $eval_func_implementation
 476 $evalf_func_implementation
 477 $derivative_func_implementation
 478 $series_func_implementation
 479 // end of generated lines
 480
 481 function_options & function_options::set_return_type(unsigned rt, unsigned rtt)
 482 {
 483         use_return_type=true;
 484         return_type=rt;
 485         return_type_tinfo=rtt;
 486         return *this;
 487 }
 488
 489 function_options & function_options::do_not_evalf_params(void)
 490 {
 491         evalf_params_first=false;
 492         return *this;
 493 }
 494
 495 function_options & function_options::remember(unsigned size,
 496                                               unsigned assoc_size,
 497                                               unsigned strategy)
 498 {
 499         use_remember=true;
 500         remember_size=size;
 501         remember_assoc_size=assoc_size;
 502         remember_strategy=strategy;
 503         return *this;
 504 }
 505
 506 function_options & function_options::overloaded(unsigned o)
 507 {
 508         functions_with_same_name=o;
 509         return *this;
 510 }
 511
 512 void function_options::test_and_set_nparams(unsigned n)
 513 {
 514         if (nparams==0) {
 515                 nparams=n;
 516         } else if (nparams!=n) {
 517                 // we do not throw an exception here because this code is
 518                 // usually executed before main(), so the exception could not
 519                 // caught anyhow
 520                 std::cerr << "WARNING: number of parameters ("
 521                           << n << ") differs from number set before ("
 522                           << nparams << ")" << std::endl;
 523         }
 524 }
 525
 526 GINAC_IMPLEMENT_REGISTERED_CLASS(function, exprseq)
 527
 528 //////////
 529 // default ctor, dtor, copy ctor assignment operator and helpers
 530 //////////
 531
 532 // public
 533
 534 function::function() : serial(0)
 535 {
 536         debugmsg("function default ctor",LOGLEVEL_CONSTRUCT);
 537         tinfo_key = TINFO_function;
 538 }
 539
 540 // protected
 541
 542 void function::copy(const function & other)
 543 {
 544         exprseq::copy(other);
 545         serial=other.serial;
 546 }
 547
 548 void function::destroy(bool call_parent)
 549 {
 550         if (call_parent) exprseq::destroy(call_parent);
 551 }
 552
 553 //////////
 554 // other ctors
 555 //////////
 556
 557 // public
 558
 559 function::function(unsigned ser) : serial(ser)
 560 {
 561         debugmsg("function ctor from unsigned",LOGLEVEL_CONSTRUCT);
 562         tinfo_key = TINFO_function;
 563 }
 564
 565 // the following lines have been generated for max. ${maxargs} parameters
 566 $constructors_implementation
 567 // end of generated lines
 568
 569 function::function(unsigned ser, const exprseq & es) : exprseq(es), serial(ser)
 570 {
 571         debugmsg("function ctor from unsigned,exprseq",LOGLEVEL_CONSTRUCT);
 572         tinfo_key = TINFO_function;
 573 }
 574
 575 function::function(unsigned ser, const exvector & v, bool discardable)
 576   : exprseq(v,discardable), serial(ser)
 577 {
 578         debugmsg("function ctor from string,exvector,bool",LOGLEVEL_CONSTRUCT);
 579         tinfo_key = TINFO_function;
 580 }
 581
 582 function::function(unsigned ser, exvector * vp)
 583   : exprseq(vp), serial(ser)
 584 {
 585         debugmsg("function ctor from unsigned,exvector *",LOGLEVEL_CONSTRUCT);
 586         tinfo_key = TINFO_function;
 587 }
 588
 589 //////////
 590 // archiving
 591 //////////
 592
 593 /** Construct object from archive_node. */
 594 function::function(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
 595 {
 596         debugmsg("function ctor from archive_node", LOGLEVEL_CONSTRUCT);
 597
 598         // Find serial number by function name
 599         std::string s;
 600         if (n.find_string("name", s)) {
 601                 unsigned int ser = 0;
 602                 std::vector<function_options>::const_iterator i = registered_functions().begin(), iend = registered_functions().end();
 603                 while (i != iend) {
 604                         if (s == i->name) {
 605                                 serial = ser;
 606                                 return;
 607                         }
 608                         i++; ser++;
 609                 }
 610                 throw (std::runtime_error("unknown function '" + s + "' in archive"));
 611         } else
 612                 throw (std::runtime_error("unnamed function in archive"));
 613 }
 614
 615 /** Unarchive the object. */
 616 ex function::unarchive(const archive_node &n, const lst &sym_lst)
 617 {
 618         return (new function(n, sym_lst))->setflag(status_flags::dynallocated);
 619 }
 620
 621 /** Archive the object. */
 622 void function::archive(archive_node &n) const
 623 {
 624         inherited::archive(n);
 625         GINAC_ASSERT(serial < registered_functions().size());
 626         n.add_string("name", registered_functions()[serial].name);
 627 }
 628
 629 //////////
 630 // functions overriding virtual functions from bases classes
 631 //////////
 632
 633 // public
 634
 635 void function::print(const print_context & c, unsigned level) const
 636 {
 637         debugmsg("function print", LOGLEVEL_PRINT);
 638
 639         GINAC_ASSERT(serial<registered_functions().size());
 640
 641         if (is_of_type(c, print_tree)) {
 642
 643                 c.s << std::string(level, ' ') << class_name() << " "
 644                     << registered_functions()[serial].name
 645                     << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
 646                     << ", nops=" << nops()
 647                     << std::endl;
 648                 unsigned delta_indent = static_cast<const print_tree &>(c).delta_indent;
 649                 for (unsigned i=0; i<nops(); ++i)
 650                         seq[i].print(c, level + delta_indent);
 651                 c.s << std::string(level + delta_indent, ' ') << "=====" << std::endl;
 652
 653         } else if (is_of_type(c, print_csrc)) {
 654
 655                 // Print function name in lowercase
 656                 std::string lname = registered_functions()[serial].name;
 657                 for (unsigned i=0; i<lname.size(); i++)
 658                         lname[i] = tolower(lname[i]);
 659                 c.s << lname << "(";
 660
 661                 // Print arguments, separated by commas
 662                 exvector::const_iterator it = seq.begin(), itend = seq.end();
 663                 while (it != itend) {
 664                         it->print(c);
 665                         it++;
 666                         if (it != itend)
 667                                 c.s << ",";
 668                 }
 669                 c.s << ")";
 670
 671         } else {
 672                 c.s << registered_functions()[serial].name;
 673                 printseq(c, '(', ',', ')', exprseq::precedence, function::precedence);
 674         }
 675 }
 676
 677 ex function::expand(unsigned options) const
 678 {
 679         return this->setflag(status_flags::expanded);
 680 }
 681
 682 int function::degree(const ex & s) const
 683 {
 684         return is_equal(*s.bp) ? 1 : 0;
 685 }
 686
 687 int function::ldegree(const ex & s) const
 688 {
 689         return is_equal(*s.bp) ? 1 : 0;
 690 }
 691
 692 ex function::coeff(const ex & s, int n) const
 693 {
 694         if (is_equal(*s.bp))
 695                 return n==1 ? _ex1() : _ex0();
 696         else
 697                 return n==0 ? ex(*this) : _ex0();
 698 }
 699
 700 ex function::eval(int level) const
 701 {
 702         GINAC_ASSERT(serial<registered_functions().size());
 703
 704         if (level>1) {
 705                 // first evaluate children, then we will end up here again
 706                 return function(serial,evalchildren(level));
 707         }
 708
 709         if (registered_functions()[serial].eval_f==0) {
 710                 return this->hold();
 711         }
 712
 713         bool use_remember=registered_functions()[serial].use_remember;
 714         ex eval_result;
 715         if (use_remember && lookup_remember_table(eval_result)) {
 716                 return eval_result;
 717         }
 718
 719         switch (registered_functions()[serial].nparams) {
 720                 // the following lines have been generated for max. ${maxargs} parameters
 721 ${eval_switch_statement}
 722                 // end of generated lines
 723         default:
 724                 throw(std::logic_error("function::eval(): invalid nparams"));
 725         }
 726         if (use_remember) {
 727                 store_remember_table(eval_result);
 728         }
 729         return eval_result;
 730 }
 731
 732 ex function::evalf(int level) const
 733 {
 734         GINAC_ASSERT(serial<registered_functions().size());
 735
 736         exvector eseq=evalfchildren(level);
 737
 738         if (registered_functions()[serial].evalf_f==0) {
 739                 return function(serial,eseq).hold();
 740         }
 741         switch (registered_functions()[serial].nparams) {
 742                 // the following lines have been generated for max. ${maxargs} parameters
 743 ${evalf_switch_statement}
 744                 // end of generated lines
 745         }
 746         throw(std::logic_error("function::evalf(): invalid nparams"));
 747 }
 748
 749 unsigned function::calchash(void) const
 750 {
 751         unsigned v = golden_ratio_hash(golden_ratio_hash(tinfo()) ^ serial);
 752         for (unsigned i=0; i<nops(); i++) {
 753                 v = rotate_left_31(v);
 754                 v ^= this->op(i).gethash();
 755         }
 756         v &= 0x7FFFFFFFU;
 757         if (flags & status_flags::evaluated) {
 758                 setflag(status_flags::hash_calculated);
 759                 hashvalue = v;
 760         }
 761         return v;
 762 }
 763
 764 ex function::thisexprseq(const exvector & v) const
 765 {
 766         return function(serial,v);
 767 }
 768
 769 ex function::thisexprseq(exvector * vp) const
 770 {
 771         return function(serial,vp);
 772 }
 773
 774 /** Implementation of ex::series for functions.
 775  *  \@see ex::series */
 776 ex function::series(const relational & r, int order, unsigned options) const
 777 {
 778         GINAC_ASSERT(serial<registered_functions().size());
 779
 780         if (registered_functions()[serial].series_f==0) {
 781                 return basic::series(r, order);
 782         }
 783         ex res;
 784         switch (registered_functions()[serial].nparams) {
 785                 // the following lines have been generated for max. ${maxargs} parameters
 786 ${series_switch_statement}
 787                 // end of generated lines
 788         }
 789         throw(std::logic_error("function::series(): invalid nparams"));
 790 }
 791
 792 // protected
 793
 794
 795 /** Implementation of ex::diff() for functions. It applies the chain rule,
 796  *  except for the Order term function.
 797  *  \@see ex::diff */
 798 ex function::derivative(const symbol & s) const
 799 {
 800         ex result;
 801
 802         if (serial == function_index_Order) {
 803                 // Order Term function only differentiates the argument
 804                 return Order(seq[0].diff(s));
 805         } else if (serial == function_index_Derivative) {
 806                 // Inert derivative performs chain rule on the first argument only, and
 807                 // adds differentiation parameter to list (second argument)
 808                 GINAC_ASSERT(is_ex_exactly_of_type(seq[0], function));
 809                 GINAC_ASSERT(is_ex_exactly_of_type(seq[1], function));
 810                 ex fcn = seq[0];
 811                 ex arg_diff;
 812                 for (unsigned i=0; i!=fcn.nops(); i++) {
 813                         arg_diff = fcn.op(i).diff(s);
 814                         if (!arg_diff.is_zero()) {
 815                                 lst new_lst = ex_to_lst(seq[1]);
 816                                 new_lst.append(i);
 817                                 result += arg_diff * Derivative(fcn, new_lst);
 818                         }
 819                 }
 820         } else {
 821                 // Chain rule
 822                 ex arg_diff;
 823                 for (unsigned i=0; i!=seq.size(); i++) {
 824                         arg_diff = seq[i].diff(s);
 825                         // We apply the chain rule only when it makes sense.  This is not
 826                         // just for performance reasons but also to allow functions to
 827                         // throw when differentiated with respect to one of its arguments
 828                         // without running into trouble with our automatic full
 829                         // differentiation:
 830                         if (!arg_diff.is_zero())
 831                                 result += pderivative(i)*arg_diff;
 832                 }
 833         }
 834         return result;
 835 }
 836
 837 int function::compare_same_type(const basic & other) const
 838 {
 839         GINAC_ASSERT(is_of_type(other, function));
 840         const function & o=static_cast<function &>(const_cast<basic &>(other));
 841
 842         if (serial!=o.serial) {
 843                 return serial < o.serial ? -1 : 1;
 844         }
 845         return exprseq::compare_same_type(o);
 846 }
 847
 848 bool function::is_equal_same_type(const basic & other) const
 849 {
 850         GINAC_ASSERT(is_of_type(other, function));
 851         const function & o=static_cast<function &>(const_cast<basic &>(other));
 852
 853         if (serial!=o.serial) return false;
 854         return exprseq::is_equal_same_type(o);
 855 }
 856
 857 unsigned function::return_type(void) const
 858 {
 859         if (seq.size()==0) {
 860                 return return_types::commutative;
 861         }
 862         return (*seq.begin()).return_type();
 863 }
 864
 865 unsigned function::return_type_tinfo(void) const
 866 {
 867         if (seq.size()==0) {
 868                 return tinfo_key;
 869         }
 870         return (*seq.begin()).return_type_tinfo();
 871 }
 872
 873 //////////
 874 // new virtual functions which can be overridden by derived classes
 875 //////////
 876
 877 // none
 878
 879 //////////
 880 // non-virtual functions in this class
 881 //////////
 882
 883 // protected
 884
 885 ex function::pderivative(unsigned diff_param) const // partial differentiation
 886 {
 887         GINAC_ASSERT(serial<registered_functions().size());
 888
 889         if (registered_functions()[serial].derivative_f==0) {
 890                 return Derivative(*this, lst(ex(diff_param)));
 891         }
 892         switch (registered_functions()[serial].nparams) {
 893                 // the following lines have been generated for max. ${maxargs} parameters
 894 ${diff_switch_statement}
 895                 // end of generated lines
 896         }
 897         throw(std::logic_error("function::pderivative(): no diff function defined"));
 898 }
 899
 900 std::vector<function_options> & function::registered_functions(void)
 901 {
 902         static std::vector<function_options> * rf = new std::vector<function_options>;
 903         return *rf;
 904 }
 905
 906 bool function::lookup_remember_table(ex & result) const
 907 {
 908         return remember_table::remember_tables()[serial].lookup_entry(*this,result);
 909 }
 910
 911 void function::store_remember_table(ex const & result) const
 912 {
 913         remember_table::remember_tables()[serial].add_entry(*this,result);
 914 }
 915
 916 // public
 917
 918 unsigned function::register_new(function_options const & opt)
 919 {
 920         unsigned same_name=0;
 921         for (unsigned i=0; i<registered_functions().size(); ++i) {
 922                 if (registered_functions()[i].name==opt.name) {
 923                         same_name++;
 924                 }
 925         }
 926         if (same_name>=opt.functions_with_same_name) {
 927                 // we do not throw an exception here because this code is
 928                 // usually executed before main(), so the exception could not
 929                 // caught anyhow
 930                 std::cerr << "WARNING: function name " << opt.name
 931                                   << " already in use!" << std::endl;
 932         }
 933         registered_functions().push_back(opt);
 934         if (opt.use_remember) {
 935                 remember_table::remember_tables().
 936                         push_back(remember_table(opt.remember_size,
 937                                                                          opt.remember_assoc_size,
 938                                                                          opt.remember_strategy));
 939         } else {
 940                 remember_table::remember_tables().push_back(remember_table());
 941         }
 942         return registered_functions().size()-1;
 943 }
 944
 945 /** Find serial number of function by name and number of parameters.
 946  *  Throws exception if function was not found. */
 947 unsigned function::find_function(const std::string &name, unsigned nparams)
 948 {
 949         std::vector<function_options>::const_iterator i = function::registered_functions().begin(), end = function::registered_functions().end();
 950         unsigned serial = 0;
 951         while (i != end) {
 952                 if (i->get_name() == name && i->get_nparams() == nparams)
 953                         return serial;
 954                 i++;
 955                 serial++;
 956         }
 957         throw (std::runtime_error("no function '" + name + "' with " + ToString(nparams) + " parameters defined"));
 958 }
 959
 960 } // namespace GiNaC
 961
 962 END_OF_IMPLEMENTATION
 963
 964 print "Creating interface file function.h...";
 965 open OUT,">function.h" or die "cannot open function.h";
 966 print OUT $interface;
 967 close OUT;
 968 print "ok.\n";
 969
 970 print "Creating implementation file function.cpp...";
 971 open OUT,">function.cpp" or die "cannot open function.cpp";
 972 print OUT $implementation;
 973 close OUT;
 974 print "ok.\n";
 975
 976 print "done.\n";