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 get_serial(void) const {return serial;}
 366         std::string get_name(void) const;
 367
 368 // member variables
 369
 370 protected:
 371         unsigned serial;
 372 };
 373
 374 // utility functions/macros
 375 inline const function &ex_to_function(const ex &e)
 376 {
 377         return static_cast<const function &>(*e.bp);
 378 }
 379
 380 #define is_ex_the_function(OBJ, FUNCNAME) \\
 381         (is_ex_exactly_of_type(OBJ, function) && static_cast<GiNaC::function *>(OBJ.bp)->get_serial() == function_index_##FUNCNAME)
 382
 383 } // namespace GiNaC
 384
 385 #endif // ndef __GINAC_FUNCTION_H__
 386
 387 END_OF_INTERFACE
 388
 389 $implementation=<<END_OF_IMPLEMENTATION;
 390 /** \@file function.cpp
 391  *
 392  *  Implementation of class function. */
 393
 394 /*
 395  *  This file was generated automatically by function.pl.
 396  *  Please do not modify it directly, edit the perl script instead!
 397  *  function.pl options: \$maxargs=${maxargs}
 398  *
 399  *  GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
 400  *
 401  *  This program is free software; you can redistribute it and/or modify
 402  *  it under the terms of the GNU General Public License as published by
 403  *  the Free Software Foundation; either version 2 of the License, or
 404  *  (at your option) any later version.
 405  *
 406  *  This program is distributed in the hope that it will be useful,
 407  *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 408  *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 409  *  GNU General Public License for more details.
 410  *
 411  *  You should have received a copy of the GNU General Public License
 412  *  along with this program; if not, write to the Free Software
 413  *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 414  */
 415
 416 #include <string>
 417 #include <stdexcept>
 418 #include <list>
 419
 420 #include "function.h"
 421 #include "ex.h"
 422 #include "lst.h"
 423 #include "print.h"
 424 #include "archive.h"
 425 #include "inifcns.h"
 426 #include "utils.h"
 427 #include "debugmsg.h"
 428 #include "remember.h"
 429
 430 namespace GiNaC {
 431
 432 //////////
 433 // helper class function_options
 434 //////////
 435
 436 function_options::function_options()
 437 {
 438         initialize();
 439 }
 440
 441 function_options::function_options(std::string const & n, std::string const & tn)
 442 {
 443         initialize();
 444         set_name(n,tn);
 445 }
 446
 447 function_options::~function_options()
 448 {
 449         // nothing to clean up at the moment
 450 }
 451
 452 void function_options::initialize(void)
 453 {
 454         set_name("unnamed_function","\\\\operatorname{unnamed}");
 455         nparams=0;
 456         eval_f=evalf_f=derivative_f=series_f=0;
 457         evalf_params_first=true;
 458         use_return_type=false;
 459         use_remember=false;
 460         functions_with_same_name=1;
 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="\\\\operatorname{"+name+"}";
 469         } else {
 470                 TeX_name=tn;
 471         }
 472         return *this;
 473 }
 474
 475 // the following lines have been generated for max. ${maxargs} parameters
 476 $eval_func_implementation
 477 $evalf_func_implementation
 478 $derivative_func_implementation
 479 $series_func_implementation
 480 // end of generated lines
 481
 482 function_options & function_options::set_return_type(unsigned rt, unsigned rtt)
 483 {
 484         use_return_type=true;
 485         return_type=rt;
 486         return_type_tinfo=rtt;
 487         return *this;
 488 }
 489
 490 function_options & function_options::do_not_evalf_params(void)
 491 {
 492         evalf_params_first=false;
 493         return *this;
 494 }
 495
 496 function_options & function_options::remember(unsigned size,
 497                                               unsigned assoc_size,
 498                                               unsigned strategy)
 499 {
 500         use_remember=true;
 501         remember_size=size;
 502         remember_assoc_size=assoc_size;
 503         remember_strategy=strategy;
 504         return *this;
 505 }
 506
 507 function_options & function_options::overloaded(unsigned o)
 508 {
 509         functions_with_same_name=o;
 510         return *this;
 511 }
 512
 513 void function_options::test_and_set_nparams(unsigned n)
 514 {
 515         if (nparams==0) {
 516                 nparams=n;
 517         } else if (nparams!=n) {
 518                 // we do not throw an exception here because this code is
 519                 // usually executed before main(), so the exception could not
 520                 // caught anyhow
 521                 std::cerr << "WARNING: number of parameters ("
 522                           << n << ") differs from number set before ("
 523                           << nparams << ")" << std::endl;
 524         }
 525 }
 526
 527 GINAC_IMPLEMENT_REGISTERED_CLASS(function, exprseq)
 528
 529 //////////
 530 // default ctor, dtor, copy ctor assignment operator and helpers
 531 //////////
 532
 533 // public
 534
 535 function::function() : serial(0)
 536 {
 537         debugmsg("function default ctor",LOGLEVEL_CONSTRUCT);
 538         tinfo_key = TINFO_function;
 539 }
 540
 541 // protected
 542
 543 void function::copy(const function & other)
 544 {
 545         exprseq::copy(other);
 546         serial=other.serial;
 547 }
 548
 549 void function::destroy(bool call_parent)
 550 {
 551         if (call_parent) exprseq::destroy(call_parent);
 552 }
 553
 554 //////////
 555 // other ctors
 556 //////////
 557
 558 // public
 559
 560 function::function(unsigned ser) : serial(ser)
 561 {
 562         debugmsg("function ctor from unsigned",LOGLEVEL_CONSTRUCT);
 563         tinfo_key = TINFO_function;
 564 }
 565
 566 // the following lines have been generated for max. ${maxargs} parameters
 567 $constructors_implementation
 568 // end of generated lines
 569
 570 function::function(unsigned ser, const exprseq & es) : exprseq(es), serial(ser)
 571 {
 572         debugmsg("function ctor from unsigned,exprseq",LOGLEVEL_CONSTRUCT);
 573         tinfo_key = TINFO_function;
 574 }
 575
 576 function::function(unsigned ser, const exvector & v, bool discardable)
 577   : exprseq(v,discardable), serial(ser)
 578 {
 579         debugmsg("function ctor from string,exvector,bool",LOGLEVEL_CONSTRUCT);
 580         tinfo_key = TINFO_function;
 581 }
 582
 583 function::function(unsigned ser, exvector * vp)
 584   : exprseq(vp), serial(ser)
 585 {
 586         debugmsg("function ctor from unsigned,exvector *",LOGLEVEL_CONSTRUCT);
 587         tinfo_key = TINFO_function;
 588 }
 589
 590 //////////
 591 // archiving
 592 //////////
 593
 594 /** Construct object from archive_node. */
 595 function::function(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
 596 {
 597         debugmsg("function ctor from archive_node", LOGLEVEL_CONSTRUCT);
 598
 599         // Find serial number by function name
 600         std::string s;
 601         if (n.find_string("name", s)) {
 602                 unsigned int ser = 0;
 603                 std::vector<function_options>::const_iterator i = registered_functions().begin(), iend = registered_functions().end();
 604                 while (i != iend) {
 605                         if (s == i->name) {
 606                                 serial = ser;
 607                                 return;
 608                         }
 609                         i++; ser++;
 610                 }
 611                 throw (std::runtime_error("unknown function '" + s + "' in archive"));
 612         } else
 613                 throw (std::runtime_error("unnamed function in archive"));
 614 }
 615
 616 /** Unarchive the object. */
 617 ex function::unarchive(const archive_node &n, const lst &sym_lst)
 618 {
 619         return (new function(n, sym_lst))->setflag(status_flags::dynallocated);
 620 }
 621
 622 /** Archive the object. */
 623 void function::archive(archive_node &n) const
 624 {
 625         inherited::archive(n);
 626         GINAC_ASSERT(serial < registered_functions().size());
 627         n.add_string("name", registered_functions()[serial].name);
 628 }
 629
 630 //////////
 631 // functions overriding virtual functions from bases classes
 632 //////////
 633
 634 // public
 635
 636 void function::print(const print_context & c, unsigned level) const
 637 {
 638         debugmsg("function print", LOGLEVEL_PRINT);
 639
 640         GINAC_ASSERT(serial<registered_functions().size());
 641
 642         if (is_of_type(c, print_tree)) {
 643
 644                 c.s << std::string(level, ' ') << class_name() << " "
 645                     << registered_functions()[serial].name
 646                     << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
 647                     << ", nops=" << nops()
 648                     << std::endl;
 649                 unsigned delta_indent = static_cast<const print_tree &>(c).delta_indent;
 650                 for (unsigned i=0; i<nops(); ++i)
 651                         seq[i].print(c, level + delta_indent);
 652                 c.s << std::string(level + delta_indent, ' ') << "=====" << std::endl;
 653
 654         } else if (is_of_type(c, print_csrc)) {
 655
 656                 // Print function name in lowercase
 657                 std::string lname = registered_functions()[serial].name;
 658                 for (unsigned i=0; i<lname.size(); i++)
 659                         lname[i] = tolower(lname[i]);
 660                 c.s << lname << "(";
 661
 662                 // Print arguments, separated by commas
 663                 exvector::const_iterator it = seq.begin(), itend = seq.end();
 664                 while (it != itend) {
 665                         it->print(c);
 666                         it++;
 667                         if (it != itend)
 668                                 c.s << ",";
 669                 }
 670                 c.s << ")";
 671
 672         } else {
 673                 c.s << registered_functions()[serial].name;
 674                 printseq(c, '(', ',', ')', exprseq::precedence, function::precedence);
 675         }
 676 }
 677
 678 ex function::expand(unsigned options) const
 679 {
 680         return this->setflag(status_flags::expanded);
 681 }
 682
 683 int function::degree(const ex & s) const
 684 {
 685         return is_equal(*s.bp) ? 1 : 0;
 686 }
 687
 688 int function::ldegree(const ex & s) const
 689 {
 690         return is_equal(*s.bp) ? 1 : 0;
 691 }
 692
 693 ex function::coeff(const ex & s, int n) const
 694 {
 695         if (is_equal(*s.bp))
 696                 return n==1 ? _ex1() : _ex0();
 697         else
 698                 return n==0 ? ex(*this) : _ex0();
 699 }
 700
 701 ex function::eval(int level) const
 702 {
 703         GINAC_ASSERT(serial<registered_functions().size());
 704
 705         if (level>1) {
 706                 // first evaluate children, then we will end up here again
 707                 return function(serial,evalchildren(level));
 708         }
 709
 710         if (registered_functions()[serial].eval_f==0) {
 711                 return this->hold();
 712         }
 713
 714         bool use_remember=registered_functions()[serial].use_remember;
 715         ex eval_result;
 716         if (use_remember && lookup_remember_table(eval_result)) {
 717                 return eval_result;
 718         }
 719
 720         switch (registered_functions()[serial].nparams) {
 721                 // the following lines have been generated for max. ${maxargs} parameters
 722 ${eval_switch_statement}
 723                 // end of generated lines
 724         default:
 725                 throw(std::logic_error("function::eval(): invalid nparams"));
 726         }
 727         if (use_remember) {
 728                 store_remember_table(eval_result);
 729         }
 730         return eval_result;
 731 }
 732
 733 ex function::evalf(int level) const
 734 {
 735         GINAC_ASSERT(serial<registered_functions().size());
 736
 737         exvector eseq=evalfchildren(level);
 738
 739         if (registered_functions()[serial].evalf_f==0) {
 740                 return function(serial,eseq).hold();
 741         }
 742         switch (registered_functions()[serial].nparams) {
 743                 // the following lines have been generated for max. ${maxargs} parameters
 744 ${evalf_switch_statement}
 745                 // end of generated lines
 746         }
 747         throw(std::logic_error("function::evalf(): invalid nparams"));
 748 }
 749
 750 unsigned function::calchash(void) const
 751 {
 752         unsigned v = golden_ratio_hash(golden_ratio_hash(tinfo()) ^ serial);
 753         for (unsigned i=0; i<nops(); i++) {
 754                 v = rotate_left_31(v);
 755                 v ^= this->op(i).gethash();
 756         }
 757         v &= 0x7FFFFFFFU;
 758         if (flags & status_flags::evaluated) {
 759                 setflag(status_flags::hash_calculated);
 760                 hashvalue = v;
 761         }
 762         return v;
 763 }
 764
 765 ex function::thisexprseq(const exvector & v) const
 766 {
 767         return function(serial,v);
 768 }
 769
 770 ex function::thisexprseq(exvector * vp) const
 771 {
 772         return function(serial,vp);
 773 }
 774
 775 /** Implementation of ex::series for functions.
 776  *  \@see ex::series */
 777 ex function::series(const relational & r, int order, unsigned options) const
 778 {
 779         GINAC_ASSERT(serial<registered_functions().size());
 780
 781         if (registered_functions()[serial].series_f==0) {
 782                 return basic::series(r, order);
 783         }
 784         ex res;
 785         switch (registered_functions()[serial].nparams) {
 786                 // the following lines have been generated for max. ${maxargs} parameters
 787 ${series_switch_statement}
 788                 // end of generated lines
 789         }
 790         throw(std::logic_error("function::series(): invalid nparams"));
 791 }
 792
 793 // protected
 794
 795
 796 /** Implementation of ex::diff() for functions. It applies the chain rule,
 797  *  except for the Order term function.
 798  *  \@see ex::diff */
 799 ex function::derivative(const symbol & s) const
 800 {
 801         ex result;
 802
 803         if (serial == function_index_Order) {
 804                 // Order Term function only differentiates the argument
 805                 return Order(seq[0].diff(s));
 806         } else if (serial == function_index_Derivative) {
 807                 // Inert derivative performs chain rule on the first argument only, and
 808                 // adds differentiation parameter to list (second argument)
 809                 GINAC_ASSERT(is_ex_exactly_of_type(seq[0], function));
 810                 GINAC_ASSERT(is_ex_exactly_of_type(seq[1], function));
 811                 ex fcn = seq[0];
 812                 ex arg_diff;
 813                 for (unsigned i=0; i!=fcn.nops(); i++) {
 814                         arg_diff = fcn.op(i).diff(s);
 815                         if (!arg_diff.is_zero()) {
 816                                 lst new_lst = ex_to_lst(seq[1]);
 817                                 new_lst.append(i);
 818                                 result += arg_diff * Derivative(fcn, new_lst);
 819                         }
 820                 }
 821         } else {
 822                 // Chain rule
 823                 ex arg_diff;
 824                 for (unsigned i=0; i!=seq.size(); i++) {
 825                         arg_diff = seq[i].diff(s);
 826                         // We apply the chain rule only when it makes sense.  This is not
 827                         // just for performance reasons but also to allow functions to
 828                         // throw when differentiated with respect to one of its arguments
 829                         // without running into trouble with our automatic full
 830                         // differentiation:
 831                         if (!arg_diff.is_zero())
 832                                 result += pderivative(i)*arg_diff;
 833                 }
 834         }
 835         return result;
 836 }
 837
 838 int function::compare_same_type(const basic & other) const
 839 {
 840         GINAC_ASSERT(is_of_type(other, function));
 841         const function & o=static_cast<function &>(const_cast<basic &>(other));
 842
 843         if (serial!=o.serial) {
 844                 return serial < o.serial ? -1 : 1;
 845         }
 846         return exprseq::compare_same_type(o);
 847 }
 848
 849 bool function::is_equal_same_type(const basic & other) const
 850 {
 851         GINAC_ASSERT(is_of_type(other, function));
 852         const function & o=static_cast<function &>(const_cast<basic &>(other));
 853
 854         if (serial!=o.serial) return false;
 855         return exprseq::is_equal_same_type(o);
 856 }
 857
 858 unsigned function::return_type(void) const
 859 {
 860         if (seq.size()==0) {
 861                 return return_types::commutative;
 862         }
 863         return (*seq.begin()).return_type();
 864 }
 865
 866 unsigned function::return_type_tinfo(void) const
 867 {
 868         if (seq.size()==0) {
 869                 return tinfo_key;
 870         }
 871         return (*seq.begin()).return_type_tinfo();
 872 }
 873
 874 //////////
 875 // new virtual functions which can be overridden by derived classes
 876 //////////
 877
 878 // none
 879
 880 //////////
 881 // non-virtual functions in this class
 882 //////////
 883
 884 // protected
 885
 886 ex function::pderivative(unsigned diff_param) const // partial differentiation
 887 {
 888         GINAC_ASSERT(serial<registered_functions().size());
 889
 890         if (registered_functions()[serial].derivative_f==0) {
 891                 return Derivative(*this, lst(ex(diff_param)));
 892         }
 893         switch (registered_functions()[serial].nparams) {
 894                 // the following lines have been generated for max. ${maxargs} parameters
 895 ${diff_switch_statement}
 896                 // end of generated lines
 897         }
 898         throw(std::logic_error("function::pderivative(): no diff function defined"));
 899 }
 900
 901 std::vector<function_options> & function::registered_functions(void)
 902 {
 903         static std::vector<function_options> * rf = new std::vector<function_options>;
 904         return *rf;
 905 }
 906
 907 bool function::lookup_remember_table(ex & result) const
 908 {
 909         return remember_table::remember_tables()[serial].lookup_entry(*this,result);
 910 }
 911
 912 void function::store_remember_table(ex const & result) const
 913 {
 914         remember_table::remember_tables()[serial].add_entry(*this,result);
 915 }
 916
 917 // public
 918
 919 unsigned function::register_new(function_options const & opt)
 920 {
 921         unsigned same_name=0;
 922         for (unsigned i=0; i<registered_functions().size(); ++i) {
 923                 if (registered_functions()[i].name==opt.name) {
 924                         same_name++;
 925                 }
 926         }
 927         if (same_name>=opt.functions_with_same_name) {
 928                 // we do not throw an exception here because this code is
 929                 // usually executed before main(), so the exception could not
 930                 // caught anyhow
 931                 std::cerr << "WARNING: function name " << opt.name
 932                                   << " already in use!" << std::endl;
 933         }
 934         registered_functions().push_back(opt);
 935         if (opt.use_remember) {
 936                 remember_table::remember_tables().
 937                         push_back(remember_table(opt.remember_size,
 938                                                                          opt.remember_assoc_size,
 939                                                                          opt.remember_strategy));
 940         } else {
 941                 remember_table::remember_tables().push_back(remember_table());
 942         }
 943         return registered_functions().size()-1;
 944 }
 945
 946 /** Find serial number of function by name and number of parameters.
 947  *  Throws exception if function was not found. */
 948 unsigned function::find_function(const std::string &name, unsigned nparams)
 949 {
 950         std::vector<function_options>::const_iterator i = function::registered_functions().begin(), end = function::registered_functions().end();
 951         unsigned serial = 0;
 952         while (i != end) {
 953                 if (i->get_name() == name && i->get_nparams() == nparams)
 954                         return serial;
 955                 i++;
 956                 serial++;
 957         }
 958         throw (std::runtime_error("no function '" + name + "' with " + ToString(nparams) + " parameters defined"));
 959 }
 960
 961 /** Return the print name of the function. */
 962 std::string function::get_name(void) const
 963 {
 964         GINAC_ASSERT(serial<registered_functions().size());
 965         return registered_functions()[serial].name;
 966 }
 967
 968 } // namespace GiNaC
 969
 970 END_OF_IMPLEMENTATION
 971
 972 print "Creating interface file function.h...";
 973 open OUT,">function.h" or die "cannot open function.h";
 974 print OUT $interface;
 975 close OUT;
 976 print "ok.\n";
 977
 978 print "Creating implementation file function.cpp...";
 979 open OUT,">function.cpp" or die "cannot open function.cpp";
 980 print OUT $implementation;
 981 close OUT;
 982 print "ok.\n";
 983
 984 print "done.\n";