Convert function.pl into C++ (well, almost) source and header.
authorAlexei Sheplyakov <Alexei.Sheplyakov@gmail.com>
Sun, 29 May 2011 12:26:37 +0000 (15:26 +0300)
committerAlexei Sheplyakov <Alexei.Sheplyakov@gmail.com>
Tue, 17 Jul 2012 04:49:44 +0000 (07:49 +0300)
The code is much more readable now, as it's (almost) plain C++ (except
simple pythonic `preprocessor' instructions). As a side effect perl is
no longer necessary for building GiNaC.

configure.ac
ginac/Makefile.am
ginac/function.cppy [new file with mode: 0644]
ginac/function.hppy [new file with mode: 0644]
ginac/function.pl [deleted file]
ginac/function.py [new file with mode: 0755]
ginsh/ginsh_parser.yy
scripts/yaptu.py [new file with mode: 0644]

index fc64c21..7ca6c3b 100644 (file)
@@ -101,6 +101,10 @@ dnl Check for stuff needed for building the GiNaC interactive shell (ginsh).
 AC_CHECK_HEADERS(unistd.h)
 GINAC_HAVE_RUSAGE
 GINAC_READLINE
+dnl Python is necessary for building function.{cpp,h}
+AC_PATH_PROG(PYTHON, python, "")
+AS_IF([test -z "$PYTHON" -a ! -f "$srcdir/ginac/function.cpp"],
+      [AC_MSG_ERROR([GiNaC will not compile because Python is missing])])
 
 dnl Check for dl library (needed for GiNaC::compile).
 GINAC_EXCOMPILER
index dce098d..8a3a762 100644 (file)
@@ -67,11 +67,13 @@ ginacinclude_HEADERS = ginac.h add.h archive.h assertion.h basic.h class_info.h
   parser/parser.h \
   parser/parse_context.h
 
-EXTRA_DIST = function.pl version.h.in
+EXTRA_DIST = version.h.in function.hppy function.cppy
 
-# Files which are generated by perl scripts
-$(srcdir)/function.h $(srcdir)/function.cpp: $(srcdir)/function.pl
-       cd $(srcdir) && perl -w function.pl
+BUILT_SOURCES = function.cpp function.h
+
+$(srcdir)/function.cpp: function.cppy function.py
+       $(PYTHON) $(srcdir)/function.py -o $@ $<
+
+$(srcdir)/function.h: function.hppy function.py
+       $(PYTHON) $(srcdir)/function.py -o $@ $<
 
-# Force build of headers before compilation
-$(srcdir)/add.cpp: $(srcdir)/function.h
diff --git a/ginac/function.cppy b/ginac/function.cppy
new file mode 100644 (file)
index 0000000..fb83cdc
--- /dev/null
@@ -0,0 +1,827 @@
+/** @file function.cpp
+ *
+ *  Implementation of class of symbolic functions. */
+
+/*
+ *  This file was generated automatically by function.py.
+ *  Please do not modify it directly, edit function.cppy instead!
+ *  function.py options: maxargs=@maxargs@
+ *
+ *  GiNaC Copyright (C) 1999-2010 Johannes Gutenberg University Mainz, Germany
+ *
+ *  This program is free software; you can redistribute it and/or modify
+ *  it under the terms of the GNU General Public License as published by
+ *  the Free Software Foundation; either version 2 of the License, or
+ *  (at your option) any later version.
+ *
+ *  This program is distributed in the hope that it will be useful,
+ *  but WITHOUT ANY WARRANTY; without even the implied warranty of
+ *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ *  GNU General Public License for more details.
+ *
+ *  You should have received a copy of the GNU General Public License
+ *  along with this program; if not, write to the Free Software
+ *  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
+ */
+
+#include "function.h"
+#include "operators.h"
+#include "fderivative.h"
+#include "ex.h"
+#include "lst.h"
+#include "symmetry.h"
+#include "print.h"
+#include "power.h"
+#include "archive.h"
+#include "inifcns.h"
+#include "tostring.h"
+#include "utils.h"
+#include "hash_seed.h"
+#include "remember.h"
+
+#include <iostream>
+#include <limits>
+#include <list>
+#include <stdexcept>
+#include <string>
+
+namespace GiNaC {
+
+//////////
+// helper class function_options
+//////////
+
+function_options::function_options()
+{
+       initialize();
+}
+
+function_options::function_options(std::string const & n, std::string const & tn)
+{
+       initialize();
+       set_name(n, tn);
+}
+
+function_options::function_options(std::string const & n, unsigned np)
+{
+       initialize();
+       set_name(n, std::string());
+       nparams = np;
+}
+
+function_options::~function_options()
+{
+       // nothing to clean up at the moment
+}
+
+void function_options::initialize()
+{
+       set_name("unnamed_function", "\\\\mbox{unnamed}");
+       nparams = 0;
+       eval_f = evalf_f = real_part_f = imag_part_f = conjugate_f = derivative_f
+               = power_f = series_f = 0;
+       evalf_params_first = true;
+       use_return_type = false;
+       eval_use_exvector_args = false;
+       evalf_use_exvector_args = false;
+       conjugate_use_exvector_args = false;
+       real_part_use_exvector_args = false;
+       imag_part_use_exvector_args = false;
+       derivative_use_exvector_args = false;
+       power_use_exvector_args = false;
+       series_use_exvector_args = false;
+       print_use_exvector_args = false;
+       use_remember = false;
+       functions_with_same_name = 1;
+       symtree = 0;
+}
+
+function_options & function_options::set_name(std::string const & n,
+                                              std::string const & tn)
+{
+       name = n;
+       if (tn==std::string())
+               TeX_name = "\\\\mbox{"+name+"}";
+       else
+               TeX_name = tn;
+       return *this;
+}
+
+function_options & function_options::latex_name(std::string const & tn)
+{
+       TeX_name = tn;
+       return *this;
+}
+
+// the following lines have been generated for max. @maxargs@ parameters
++++ for method, N in [ (f, N) for f in methods[0:-1] for N in range(1, maxargs + 1)]:
+function_options & function_options::@method@_func(@method@_funcp_@N@ e) 
+{
+       test_and_set_nparams(@N@);
+       @method@_f = @method@_funcp(e);
+       return *this;
+}
+---
+// end of generated lines
+
++++ for method in methods[0:-1]:
+function_options & function_options::@method@_func(@method@_funcp_exvector e)
+{
+       @method@_use_exvector_args = true;
+       @method@_f = @method@_funcp(e);
+       return *this;
+}
+---
+
+// end of generated lines
+
+function_options & function_options::set_return_type(unsigned rt, const return_type_t* rtt)
+{
+       use_return_type = true;
+       return_type = rt;
+       if (rtt != 0)
+               return_type_tinfo = *rtt;
+       else
+               return_type_tinfo = make_return_type_t<function>();
+       return *this;
+}
+
+function_options & function_options::do_not_evalf_params()
+{
+       evalf_params_first = false;
+       return *this;
+}
+
+function_options & function_options::remember(unsigned size,
+                                              unsigned assoc_size,
+                                              unsigned strategy)
+{
+       use_remember = true;
+       remember_size = size;
+       remember_assoc_size = assoc_size;
+       remember_strategy = strategy;
+       return *this;
+}
+
+function_options & function_options::overloaded(unsigned o)
+{
+       functions_with_same_name = o;
+       return *this;
+}
+
+function_options & function_options::set_symmetry(const symmetry & s)
+{
+       symtree = s;
+       return *this;
+}
+       
+void function_options::test_and_set_nparams(unsigned n)
+{
+       if (nparams==0) {
+               nparams = n;
+       } else if (nparams!=n) {
+               // we do not throw an exception here because this code is
+               // usually executed before main(), so the exception could not
+               // be caught anyhow
+               std::cerr << "WARNING: " << name << "(): number of parameters ("
+                         << n << ") differs from number set before (" 
+                         << nparams << ")" << std::endl;
+       }
+}
+
+void function_options::set_print_func(unsigned id, print_funcp f)
+{
+       if (id >= print_dispatch_table.size())
+               print_dispatch_table.resize(id + 1);
+       print_dispatch_table[id] = f;
+}
+
+/** This can be used as a hook for external applications. */
+unsigned function::current_serial = 0;
+
+
+GINAC_IMPLEMENT_REGISTERED_CLASS(function, exprseq)
+
+//////////
+// default constructor
+//////////
+
+// public
+
+function::function() : serial(0)
+{
+}
+
+//////////
+// other constructors
+//////////
+
+// public
+
+function::function(unsigned ser) : serial(ser)
+{
+}
+
+// the following lines have been generated for max. @maxargs@ parameters
++++ for N in range(1, maxargs + 1):
+function::function(unsigned ser, @seq('const ex & param%(n)d', N)@)
+       : exprseq(@seq('param%(n)d', N)@), serial(ser)
+{
+}
+---
+
+function::function(unsigned ser, const exprseq & es) : exprseq(es), serial(ser)
+{
+
+       // Force re-evaluation even if the exprseq was already evaluated
+       // (the exprseq copy constructor copies the flags)
+       clearflag(status_flags::evaluated);
+}
+
+function::function(unsigned ser, const exvector & v, bool discardable) 
+  : exprseq(v,discardable), serial(ser)
+{
+}
+
+function::function(unsigned ser, std::auto_ptr<exvector> vp) 
+  : exprseq(vp), serial(ser)
+{
+}
+
+//////////
+// archiving
+//////////
+
+/** Construct object from archive_node. */
+void function::read_archive(const archive_node& n, lst& sym_lst)
+{
+       inherited::read_archive(n, sym_lst);
+       // Find serial number by function name
+       std::string s;
+       if (n.find_string("name", s)) {
+               unsigned int ser = 0;
+               std::vector<function_options>::const_iterator i = registered_functions().begin(), iend = registered_functions().end();
+               while (i != iend) {
+                       if (s == i->name) {
+                               serial = ser;
+                               return;
+                       }
+                       ++i; ++ser;
+               }
+               throw (std::runtime_error("unknown function '" + s + "' in archive"));
+       } else
+               throw (std::runtime_error("unnamed function in archive"));
+}
+
+/** Archive the object. */
+void function::archive(archive_node &n) const
+{
+       inherited::archive(n);
+       GINAC_ASSERT(serial < registered_functions().size());
+       n.add_string("name", registered_functions()[serial].name);
+}
+
+GINAC_BIND_UNARCHIVER(function);
+
+//////////
+// functions overriding virtual functions from base classes
+//////////
+
+// public
+
+void function::print(const print_context & c, unsigned level) const
+{
+       GINAC_ASSERT(serial<registered_functions().size());
+       const function_options &opt = registered_functions()[serial];
+       const std::vector<print_funcp> &pdt = opt.print_dispatch_table;
+
+       // Dynamically dispatch on print_context type
+       const print_context_class_info *pc_info = &c.get_class_info();
+
+next_context:
+       unsigned id = pc_info->options.get_id();
+       if (id >= pdt.size() || pdt[id] == NULL) {
+
+               // Method not found, try parent print_context class
+               const print_context_class_info *parent_pc_info = pc_info->get_parent();
+               if (parent_pc_info) {
+                       pc_info = parent_pc_info;
+                       goto next_context;
+               }
+
+               // Method still not found, use default output
+               if (is_a<print_tree>(c)) {
+
+                       c.s << std::string(level, ' ') << class_name() << " "
+                           << opt.name << " @" << this
+                           << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
+                           << ", nops=" << nops()
+                           << std::endl;
+                       unsigned delta_indent = static_cast<const print_tree &>(c).delta_indent;
+                       for (size_t i=0; i<seq.size(); ++i)
+                               seq[i].print(c, level + delta_indent);
+                       c.s << std::string(level + delta_indent, ' ') << "=====" << std::endl;
+
+               } else if (is_a<print_csrc>(c)) {
+
+                       // Print function name in lowercase
+                       std::string lname = opt.name;
+                       size_t num = lname.size();
+                       for (size_t i=0; i<num; i++)
+                               lname[i] = tolower(lname[i]);
+                       c.s << lname;
+                       printseq(c, '(', ',', ')', exprseq::precedence(), function::precedence());
+
+               } else if (is_a<print_latex>(c)) {
+                       c.s << opt.TeX_name;
+                       printseq(c, '(', ',', ')', exprseq::precedence(), function::precedence());
+               } else {
+                       c.s << opt.name;
+                       printseq(c, '(', ',', ')', exprseq::precedence(), function::precedence());
+               }
+
+       } else {
+
+               // Method found, call it
+               current_serial = serial;
+               if (opt.print_use_exvector_args)
+                       ((print_funcp_exvector)pdt[id])(seq, c);
+               else switch (opt.nparams) {
+                       // the following lines have been generated for max. @maxargs@ parameters
++++ for N in range(1, maxargs + 1):
+                       case @N@:
+                               ((print_funcp_@N@)(pdt[id]))(@seq('seq[%(n)d]', N, 0)@, c);
+                               break;
+---
+                       // end of generated lines
+               default:
+                       throw(std::logic_error("function::print(): invalid nparams"));
+               }
+       }
+}
+
+ex function::expand(unsigned options) const
+{
+       // Only expand arguments when asked to do so
+       if (options & expand_options::expand_function_args)
+               return inherited::expand(options);
+       else
+               return (options == 0) ? setflag(status_flags::expanded) : *this;
+}
+
+ex function::eval(int level) const
+{
+       if (level>1) {
+               // first evaluate children, then we will end up here again
+               return function(serial,evalchildren(level));
+       }
+
+       GINAC_ASSERT(serial<registered_functions().size());
+       const function_options &opt = registered_functions()[serial];
+
+       // Canonicalize argument order according to the symmetry properties
+       if (seq.size() > 1 && !(opt.symtree.is_zero())) {
+               exvector v = seq;
+               GINAC_ASSERT(is_a<symmetry>(opt.symtree));
+               int sig = canonicalize(v.begin(), ex_to<symmetry>(opt.symtree));
+               if (sig != std::numeric_limits<int>::max()) {
+                       // Something has changed while sorting arguments, more evaluations later
+                       if (sig == 0)
+                               return _ex0;
+                       return ex(sig) * thiscontainer(v);
+               }
+       }
+
+       if (opt.eval_f==0) {
+               return this->hold();
+       }
+
+       bool use_remember = opt.use_remember;
+       ex eval_result;
+       if (use_remember && lookup_remember_table(eval_result)) {
+               return eval_result;
+       }
+       current_serial = serial;
+       if (opt.eval_use_exvector_args)
+               eval_result = ((eval_funcp_exvector)(opt.eval_f))(seq);
+       else
+       switch (opt.nparams) {
+               // the following lines have been generated for max. @maxargs@ parameters
++++ for N in range(1, maxargs + 1):
+               case @N@:
+                       eval_result = ((eval_funcp_@N@)(opt.eval_f))(@seq('seq[%(n)d]', N, 0)@);
+                       break;
+---
+               // end of generated lines
+       default:
+               throw(std::logic_error("function::eval(): invalid nparams"));
+       }
+       if (use_remember) {
+               store_remember_table(eval_result);
+       }
+       return eval_result;
+}
+
+ex function::evalf(int level) const
+{
+       GINAC_ASSERT(serial<registered_functions().size());
+       const function_options &opt = registered_functions()[serial];
+
+       // Evaluate children first
+       exvector eseq;
+       if (level == 1 || !(opt.evalf_params_first))
+               eseq = seq;
+       else if (level == -max_recursion_level)
+               throw(std::runtime_error("max recursion level reached"));
+       else {
+               eseq.reserve(seq.size());
+               --level;
+               exvector::const_iterator it = seq.begin(), itend = seq.end();
+               while (it != itend) {
+                       eseq.push_back(it->evalf(level));
+                       ++it;
+               }
+       }
+
+       if (opt.evalf_f==0) {
+               return function(serial,eseq).hold();
+       }
+       current_serial = serial;
+       if (opt.evalf_use_exvector_args)
+               return ((evalf_funcp_exvector)(opt.evalf_f))(seq);
+       switch (opt.nparams) {
+               // the following lines have been generated for max. @maxargs@ parameters
++++ for N in range(1, maxargs + 1):
+               case @N@:
+                       return ((evalf_funcp_@N@)(opt.evalf_f))(@seq('eseq[%(n)d]', N, 0)@);
+---
+               // end of generated lines
+       }
+       throw(std::logic_error("function::evalf(): invalid nparams"));
+}
+
+/**
+ *  This method is defined to be in line with behaviour of function::return_type()
+ */
+ex function::eval_ncmul(const exvector & v) const
+{
+       // If this function is called then the list of arguments is non-empty
+       // and the first argument is non-commutative, see  function::return_type()
+       return seq.begin()->eval_ncmul(v);
+}
+
+unsigned function::calchash() const
+{
+       unsigned v = golden_ratio_hash(make_hash_seed(typeid(*this)) ^ serial);
+       for (size_t i=0; i<nops(); i++) {
+               v = rotate_left(v);
+               v ^= this->op(i).gethash();
+       }
+
+       if (flags & status_flags::evaluated) {
+               setflag(status_flags::hash_calculated);
+               hashvalue = v;
+       }
+       return v;
+}
+
+ex function::thiscontainer(const exvector & v) const
+{
+       return function(serial, v);
+}
+
+ex function::thiscontainer(std::auto_ptr<exvector> vp) const
+{
+       return function(serial, vp);
+}
+
+/** Implementation of ex::series for functions.
+ *  \@see ex::series */
+ex function::series(const relational & r, int order, unsigned options) const
+{
+       GINAC_ASSERT(serial<registered_functions().size());
+       const function_options &opt = registered_functions()[serial];
+
+       if (opt.series_f==0) {
+               return basic::series(r, order);
+       }
+       ex res;
+       current_serial = serial;
+       if (opt.series_use_exvector_args) {
+               try {
+                       res = ((series_funcp_exvector)(opt.series_f))(seq, r, order, options);
+               } catch (do_taylor) {
+                       res = basic::series(r, order, options);
+               }
+               return res;
+       }
+       switch (opt.nparams) {
+               // the following lines have been generated for max. @maxargs@ parameters
++++ for N in range(1, maxargs + 1):
+               case @N@:
+                       try {
+                               res = ((series_funcp_@N@)(opt.series_f))(@seq('seq[%(n)d]', N, 0)@, r, order, options);
+                       } catch (do_taylor) {
+                               res = basic::series(r, order, options);
+                       }
+                       return res;
+---
+               // end of generated lines
+       }
+       throw(std::logic_error("function::series(): invalid nparams"));
+}
+
+/** Implementation of ex::conjugate for functions. */
+ex function::conjugate() const
+{
+       GINAC_ASSERT(serial<registered_functions().size());
+       const function_options & opt = registered_functions()[serial];
+
+       if (opt.conjugate_f==0) {
+               return conjugate_function(*this).hold();
+       }
+
+       if (opt.conjugate_use_exvector_args) {
+               return ((conjugate_funcp_exvector)(opt.conjugate_f))(seq);
+       }
+
+       switch (opt.nparams) {
+               // the following lines have been generated for max. @maxargs@ parameters
++++ for N in range(1, maxargs + 1):
+               case @N@:
+                       return ((conjugate_funcp_@N@)(opt.conjugate_f))(@seq('seq[%(n)d]', N, 0)@);
+---
+               // end of generated lines
+       }
+       throw(std::logic_error("function::conjugate(): invalid nparams"));
+}
+
+/** Implementation of ex::real_part for functions. */
+ex function::real_part() const
+{
+       GINAC_ASSERT(serial<registered_functions().size());
+       const function_options & opt = registered_functions()[serial];
+
+       if (opt.real_part_f==0)
+               return basic::real_part();
+
+       if (opt.real_part_use_exvector_args)
+               return ((real_part_funcp_exvector)(opt.real_part_f))(seq);
+
+       switch (opt.nparams) {
+               // the following lines have been generated for max. @maxargs@ parameters
++++ for N in range(1, maxargs + 1):
+               case @N@:
+                       return ((real_part_funcp_@N@)(opt.real_part_f))(@seq('seq[%(n)d]', N, 0)@);
+---
+               // end of generated lines
+       }
+       throw(std::logic_error("function::real_part(): invalid nparams"));
+}
+
+/** Implementation of ex::imag_part for functions. */
+ex function::imag_part() const
+{
+       GINAC_ASSERT(serial<registered_functions().size());
+       const function_options & opt = registered_functions()[serial];
+
+       if (opt.imag_part_f==0)
+               return basic::imag_part();
+
+       if (opt.imag_part_use_exvector_args)
+               return ((imag_part_funcp_exvector)(opt.imag_part_f))(seq);
+
+       switch (opt.nparams) {
+               // the following lines have been generated for max. @maxargs@ parameters
++++ for N in range(1, maxargs + 1):
+               case @N@:
+                       return ((imag_part_funcp_@N@)(opt.imag_part_f))(@seq('seq[%(n)d]', N, 0)@);
+---
+               // end of generated lines
+       }
+       throw(std::logic_error("function::imag_part(): invalid nparams"));
+}
+
+// protected
+
+/** Implementation of ex::diff() for functions. It applies the chain rule,
+ *  except for the Order term function.
+ *  \@see ex::diff */
+ex function::derivative(const symbol & s) const
+{
+       ex result;
+
+       if (serial == Order_SERIAL::serial) {
+               // Order Term function only differentiates the argument
+               return Order(seq[0].diff(s));
+       } else {
+               // Chain rule
+               ex arg_diff;
+               size_t num = seq.size();
+               for (size_t i=0; i<num; i++) {
+                       arg_diff = seq[i].diff(s);
+                       // We apply the chain rule only when it makes sense.  This is not
+                       // just for performance reasons but also to allow functions to
+                       // throw when differentiated with respect to one of its arguments
+                       // without running into trouble with our automatic full
+                       // differentiation:
+                       if (!arg_diff.is_zero())
+                               result += pderivative(i)*arg_diff;
+               }
+       }
+       return result;
+}
+
+int function::compare_same_type(const basic & other) const
+{
+       GINAC_ASSERT(is_a<function>(other));
+       const function & o = static_cast<const function &>(other);
+
+       if (serial != o.serial)
+               return serial < o.serial ? -1 : 1;
+       else
+               return exprseq::compare_same_type(o);
+}
+
+bool function::is_equal_same_type(const basic & other) const
+{
+       GINAC_ASSERT(is_a<function>(other));
+       const function & o = static_cast<const function &>(other);
+
+       if (serial != o.serial)
+               return false;
+       else
+               return exprseq::is_equal_same_type(o);
+}
+
+bool function::match_same_type(const basic & other) const
+{
+       GINAC_ASSERT(is_a<function>(other));
+       const function & o = static_cast<const function &>(other);
+
+       return serial == o.serial;
+}
+
+unsigned function::return_type() const
+{
+       GINAC_ASSERT(serial<registered_functions().size());
+       const function_options &opt = registered_functions()[serial];
+
+       if (opt.use_return_type) {
+               // Return type was explicitly specified
+               return opt.return_type;
+       } else {
+               // Default behavior is to use the return type of the first
+               // argument. Thus, exp() of a matrix behaves like a matrix, etc.
+               if (seq.empty())
+                       return return_types::commutative;
+               else
+                       return seq.begin()->return_type();
+       }
+}
+
+return_type_t function::return_type_tinfo() const
+{
+       GINAC_ASSERT(serial<registered_functions().size());
+       const function_options &opt = registered_functions()[serial];
+
+       if (opt.use_return_type) {
+               // Return type was explicitly specified
+               return opt.return_type_tinfo;
+       } else {
+               // Default behavior is to use the return type of the first
+               // argument. Thus, exp() of a matrix behaves like a matrix, etc.
+               if (seq.empty())
+                       return make_return_type_t<function>();
+               else
+                       return seq.begin()->return_type_tinfo();
+       }
+}
+
+//////////
+// new virtual functions which can be overridden by derived classes
+//////////
+
+// none
+
+//////////
+// non-virtual functions in this class
+//////////
+
+// protected
+
+ex function::pderivative(unsigned diff_param) const // partial differentiation
+{
+       GINAC_ASSERT(serial<registered_functions().size());
+       const function_options &opt = registered_functions()[serial];
+       
+       // No derivative defined? Then return abstract derivative object
+       if (opt.derivative_f == NULL)
+               return fderivative(serial, diff_param, seq);
+
+       current_serial = serial;
+       if (opt.derivative_use_exvector_args)
+               return ((derivative_funcp_exvector)(opt.derivative_f))(seq, diff_param);
+       switch (opt.nparams) {
+               // the following lines have been generated for max. @maxargs@ parameters
++++ for N in range(1, maxargs + 1):
+               case @N@:
+                       return ((derivative_funcp_@N@)(opt.derivative_f))(@seq('seq[%(n)d]', N, 0)@, diff_param);
+---
+               // end of generated lines
+       }
+       throw(std::logic_error("function::pderivative(): no diff function defined"));
+}
+
+ex function::power(const ex & power_param) const // power of function
+{
+       GINAC_ASSERT(serial<registered_functions().size());
+       const function_options &opt = registered_functions()[serial];
+       
+       if (opt.power_f == NULL)
+               return (new GiNaC::power(*this, power_param))->setflag(status_flags::dynallocated |
+                                                                      status_flags::evaluated);
+
+       current_serial = serial;
+       if (opt.power_use_exvector_args)
+               return ((power_funcp_exvector)(opt.power_f))(seq,  power_param);
+       switch (opt.nparams) {
+               // the following lines have been generated for max. @maxargs@ parameters
++++ for N in range(1, maxargs + 1):
+               case @N@:
+                       return ((power_funcp_@N@)(opt.power_f))(@seq('seq[%(n)d]', N, 0)@, power_param);
+---
+               // end of generated lines
+       }
+       throw(std::logic_error("function::power(): no power function defined"));
+}
+
+std::vector<function_options> & function::registered_functions()
+{
+       static std::vector<function_options> rf = std::vector<function_options>();
+       return rf;
+}
+
+bool function::lookup_remember_table(ex & result) const
+{
+       return remember_table::remember_tables()[this->serial].lookup_entry(*this,result);
+}
+
+void function::store_remember_table(ex const & result) const
+{
+       remember_table::remember_tables()[this->serial].add_entry(*this,result);
+}
+
+// public
+
+unsigned function::register_new(function_options const & opt)
+{
+       size_t same_name = 0;
+       for (size_t i=0; i<registered_functions().size(); ++i) {
+               if (registered_functions()[i].name==opt.name) {
+                       ++same_name;
+               }
+       }
+       if (same_name>=opt.functions_with_same_name) {
+               // we do not throw an exception here because this code is
+               // usually executed before main(), so the exception could not
+               // caught anyhow
+               std::cerr << "WARNING: function name " << opt.name
+                         << " already in use!" << std::endl;
+       }
+       registered_functions().push_back(opt);
+       if (opt.use_remember) {
+               remember_table::remember_tables().
+                       push_back(remember_table(opt.remember_size,
+                                                opt.remember_assoc_size,
+                                                opt.remember_strategy));
+       } else {
+               remember_table::remember_tables().push_back(remember_table());
+       }
+       return registered_functions().size()-1;
+}
+
+/** Find serial number of function by name and number of parameters.
+ *  Throws exception if function was not found. */
+unsigned function::find_function(const std::string &name, unsigned nparams)
+{
+       std::vector<function_options>::const_iterator i = function::registered_functions().begin(), end = function::registered_functions().end();
+       unsigned serial = 0;
+       while (i != end) {
+               if (i->get_name() == name && i->get_nparams() == nparams)
+                       return serial;
+               ++i;
+               ++serial;
+       }
+       throw (std::runtime_error("no function '" + name + "' with " + ToString(nparams) + " parameters defined"));
+}
+
+/** Return the print name of the function. */
+std::string function::get_name() const
+{
+       GINAC_ASSERT(serial<registered_functions().size());
+       return registered_functions()[serial].name;
+}
+
+} // namespace GiNaC
+
diff --git a/ginac/function.hppy b/ginac/function.hppy
new file mode 100644 (file)
index 0000000..e7ec83e
--- /dev/null
@@ -0,0 +1,277 @@
+/** @file function.h
+ *
+ *  Interface to class of symbolic functions. */
+
+/*
+ *  This file was generated automatically from function.hppy.
+ *  Please do not modify it directly, edit function.hppy instead!
+ *
+ *  GiNaC Copyright (C) 1999-2010 Johannes Gutenberg University Mainz, Germany
+ *
+ *  This program is free software; you can redistribute it and/or modify
+ *  it under the terms of the GNU General Public License as published by
+ *  the Free Software Foundation; either version 2 of the License, or
+ *  (at your option) any later version.
+ *
+ *  This program is distributed in the hope that it will be useful,
+ *  but WITHOUT ANY WARRANTY; without even the implied warranty of
+ *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ *  GNU General Public License for more details.
+ *
+ *  You should have received a copy of the GNU General Public License
+ *  along with this program; if not, write to the Free Software
+ *  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
+ */
+
+#ifndef GINAC_FUNCTION_H
+#define GINAC_FUNCTION_H
+
+#include "exprseq.h"
+
+// CINT needs <algorithm> to work properly with <vector>
+#include <algorithm>
+#include <string>
+#include <vector>
+
++++ for N in range(1, maxargs + 1):
+#define DECLARE_FUNCTION_@N@P(NAME) \
+class NAME##_SERIAL { public: static unsigned serial; }; \
+const unsigned NAME##_NPARAMS = @N@; \
+template< @seq('typename T%(n)d', N)@ > const GiNaC::function NAME( @seq('const T%(n)d & p%(n)d', N)@ ) { \
+       return GiNaC::function(NAME##_SERIAL::serial, @seq('GiNaC::ex(p%(n)d)', N)@ ); \
+}
+---
+// end of generated lines
+
+#define REGISTER_FUNCTION(NAME,OPT) \
+unsigned NAME##_SERIAL::serial = \
+       GiNaC::function::register_new(GiNaC::function_options(#NAME, NAME##_NPARAMS).OPT);
+
+namespace GiNaC {
+
+class function;
+class symmetry;
+
+typedef ex (* eval_funcp)();
+typedef ex (* evalf_funcp)();
+typedef ex (* conjugate_funcp)();
+typedef ex (* real_part_funcp)();
+typedef ex (* imag_part_funcp)();
+typedef ex (* derivative_funcp)();
+typedef ex (* power_funcp)();
+typedef ex (* series_funcp)();
+typedef void (* print_funcp)();
+
+// the following lines have been generated for max. @maxargs@ parameters
++++ for N, args in [ ( N, seq('const ex &', N) ) for N in range(1, maxargs + 1) ]:
+typedef ex (* eval_funcp_@N@)( @args@ );
+typedef ex (* evalf_funcp_@N@)( @args@ );
+typedef ex (* conjugate_funcp_@N@)( @args@ );
+typedef ex (* real_part_funcp_@N@)( @args@ );
+typedef ex (* imag_part_funcp_@N@)( @args@ );
+typedef ex (* derivative_funcp_@N@)( @args@, unsigned );
+typedef ex (* power_funcp_@N@)( @args@, const ex & );
+typedef ex (* series_funcp_@N@)( @args@, const relational &, int, unsigned );
+typedef void (* print_funcp_@N@)( @args@, const print_context & );
+---
+// end of generated lines
+
+// Alternatively, an exvector may be passed into the static function, instead
+// of individual ex objects.  Then, the number of arguments is not limited.
++++ for fp in "eval evalf conjugate real_part imag_part".split():
+typedef ex (* @fp@_funcp_exvector)(const exvector &);
+---
+typedef ex (* derivative_funcp_exvector)(const exvector &, unsigned);
+typedef ex (* power_funcp_exvector)(const exvector &, const ex &);
+typedef ex (* series_funcp_exvector)(const exvector &, const relational &, int, unsigned);
+typedef void (* print_funcp_exvector)(const exvector &, const print_context &);
+
+
+class function_options
+{
+       friend class function;
+       friend class fderivative;
+public:
+       function_options();
+       function_options(std::string const & n, std::string const & tn=std::string());
+       function_options(std::string const & n, unsigned np);
+       ~function_options();
+       void initialize();
+
+       function_options & dummy() { return *this; }
+       function_options & set_name(std::string const & n, std::string const & tn=std::string());
+       function_options & latex_name(std::string const & tn);
+       // following lines have been generated for max. @maxargs@ parameters
++++ for f, N in [ (f, N) for f in methods[0:-1] for N in range(1, maxargs + 1) ]:
+       function_options & @f@_func(@f@_funcp_@N@ e);
+---
++++ for f in methods[0:-1]:
+       function_options & @f@_func(@f@_funcp_exvector e);
+---
++++ for N in range(1, N + 1):
+       template <class Ctx> function_options & print_func(print_funcp_@N@ p)
+       {
+               test_and_set_nparams(@N@);
+               set_print_func(Ctx::get_class_info_static().options.get_id(), print_funcp(p));
+               return *this;
+       }
+---
+       // end of generated lines
+
+       template <class Ctx> function_options & print_func(print_funcp_exvector p)
+       {
+               print_use_exvector_args = true;
+               set_print_func(Ctx::get_class_info_static().options.get_id(), print_funcp(p));
+               return *this;
+       }
+
+       function_options & set_return_type(unsigned rt, const return_type_t* rtt = 0);
+       function_options & do_not_evalf_params();
+       function_options & remember(unsigned size, unsigned assoc_size=0,
+                                   unsigned strategy=remember_strategies::delete_never);
+       function_options & overloaded(unsigned o);
+       function_options & set_symmetry(const symmetry & s);
+
+       std::string get_name() const { return name; }
+       unsigned get_nparams() const { return nparams; }
+
+protected:
+       bool has_derivative() const { return derivative_f != NULL; }
+       bool has_power() const { return power_f != NULL; }
+       void test_and_set_nparams(unsigned n);
+       void set_print_func(unsigned id, print_funcp f);
+
+       std::string name;
+       std::string TeX_name;
+
+       unsigned nparams;
+
+       eval_funcp eval_f;
+       evalf_funcp evalf_f;
+       conjugate_funcp conjugate_f;
+       real_part_funcp real_part_f;
+       imag_part_funcp imag_part_f;
+       derivative_funcp derivative_f;
+       power_funcp power_f;
+       series_funcp series_f;
+       std::vector<print_funcp> print_dispatch_table;
+
+       bool evalf_params_first;
+
+       bool use_return_type;
+       unsigned return_type;
+       return_type_t return_type_tinfo;
+
+       bool use_remember;
+       unsigned remember_size;
+       unsigned remember_assoc_size;
+       unsigned remember_strategy;
+
+       bool eval_use_exvector_args;
+       bool evalf_use_exvector_args;
+       bool conjugate_use_exvector_args;
+       bool real_part_use_exvector_args;
+       bool imag_part_use_exvector_args;
+       bool derivative_use_exvector_args;
+       bool power_use_exvector_args;
+       bool series_use_exvector_args;
+       bool print_use_exvector_args;
+
+       unsigned functions_with_same_name;
+
+       ex symtree;
+};
+
+
+/** Exception class thrown by classes which provide their own series expansion
+ *  to signal that ordinary Taylor expansion is safe. */
+class do_taylor {};
+
+
+/** The class function is used to implement builtin functions like sin, cos...
+       and user defined functions */
+class function : public exprseq
+{
+       GINAC_DECLARE_REGISTERED_CLASS(function, exprseq)
+
+       friend class remember_table_entry;
+
+// member functions
+
+       // other constructors
+public:
+       function(unsigned ser);
+       // the following lines have been generated for max. @maxargs@ parameters
++++ for N in range(1, maxargs + 1):
+       function(unsigned ser, @seq('const ex & param%(n)d', N)@);
+---
+       // end of generated lines
+       function(unsigned ser, const exprseq & es);
+       function(unsigned ser, const exvector & v, bool discardable = false);
+       function(unsigned ser, std::auto_ptr<exvector> vp);
+       
+       // functions overriding virtual functions from base classes
+public:
+       void print(const print_context & c, unsigned level = 0) const;
+       unsigned precedence() const {return 70;}
+       ex expand(unsigned options=0) const;
+       ex eval(int level=0) const;
+       ex evalf(int level=0) const;
+       ex eval_ncmul(const exvector & v) const;
+       unsigned calchash() const;
+       ex series(const relational & r, int order, unsigned options = 0) const;
+       ex thiscontainer(const exvector & v) const;
+       ex thiscontainer(std::auto_ptr<exvector> vp) const;
+       ex conjugate() const;
+       ex real_part() const;
+       ex imag_part() const;
+       void archive(archive_node& n) const;
+       void read_archive(const archive_node& n, lst& syms);
+protected:
+       ex derivative(const symbol & s) const;
+       bool is_equal_same_type(const basic & other) const;
+       bool match_same_type(const basic & other) const;
+       unsigned return_type() const;
+       return_type_t return_type_tinfo() const;
+       
+       // new virtual functions which can be overridden by derived classes
+       // none
+       
+       // non-virtual functions in this class
+protected:
+       ex pderivative(unsigned diff_param) const; // partial differentiation
+       static std::vector<function_options> & registered_functions();
+       bool lookup_remember_table(ex & result) const;
+       void store_remember_table(ex const & result) const;
+public:
+       ex power(const ex & exp) const;
+       static unsigned register_new(function_options const & opt);
+       static unsigned current_serial;
+       static unsigned find_function(const std::string &name, unsigned nparams);
+       static std::vector<function_options> get_registered_functions() { return registered_functions(); };
+       unsigned get_serial() const {return serial;}
+       std::string get_name() const;
+
+// member variables
+
+protected:
+       unsigned serial;
+};
+GINAC_DECLARE_UNARCHIVER(function);
+
+// utility functions/macros
+
+template <typename T>
+inline bool is_the_function(const ex & x)
+{
+       return is_exactly_a<function>(x)
+           && ex_to<function>(x).get_serial() == T::serial;
+}
+
+// Check whether OBJ is the specified symbolic function.
+#define is_ex_the_function(OBJ, FUNCNAME) (GiNaC::is_the_function<FUNCNAME##_SERIAL>(OBJ))
+
+} // namespace GiNaC
+
+#endif // ndef GINAC_FUNCTION_H
+
diff --git a/ginac/function.pl b/ginac/function.pl
deleted file mode 100644 (file)
index d4a03ce..0000000
+++ /dev/null
@@ -1,1416 +0,0 @@
-#  This perl script automatically generates function.h and function.cpp
-
-#  function.pl options: \$maxargs=${maxargs}
-# 
-#  GiNaC Copyright (C) 1999-2011 Johannes Gutenberg University Mainz, Germany
-# 
-#  This program is free software; you can redistribute it and/or modify
-#  it under the terms of the GNU General Public License as published by
-#  the Free Software Foundation; either version 2 of the License, or
-#  (at your option) any later version.
-# 
-#  This program is distributed in the hope that it will be useful,
-#  but WITHOUT ANY WARRANTY; without even the implied warranty of
-#  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
-#  GNU General Public License for more details.
-# 
-#  You should have received a copy of the GNU General Public License
-#  along with this program; if not, write to the Free Software
-#  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
-
-$maxargs=14;
-
-sub generate_seq {
-       my ($seq_template,$n)=@_;
-       my ($res,$N);
-       
-       $res='';
-       for ($N=1; $N<=$n; $N++) {
-               $res .= eval('"' . $seq_template . '"');
-               if ($N!=$n) {
-                       $res .= ', ';
-               }
-       }
-       return $res;
-}
-
-sub generate_from_to {
-       my ($template,$seq_template1,$seq_template2,$seq_template3,$from,$to)=@_;
-       my ($res,$N,$SEQ);
-
-       $res='';
-       for ($N=$from; $N<=$to; $N++) {
-               $SEQ1=generate_seq($seq_template1,$N);
-               $SEQ2=generate_seq($seq_template2,$N);
-               $SEQ3=generate_seq($seq_template3,$N);
-               $res .= eval('"' . $template . '"');
-               $SEQ1=''; # to avoid main::SEQ1 used only once warning
-               $SEQ2=''; # same as above
-               $SEQ3=''; # same as above
-       }
-       return $res;
-}
-
-sub generate {
-       my ($template,$seq_template1,$seq_template2,$seq_template3)=@_;
-       return generate_from_to($template,$seq_template1,$seq_template2,$seq_template3,1,$maxargs);
-}
-
-$declare_function_macro = generate(
-       <<'END_OF_DECLARE_FUNCTION_MACRO','typename T${N}','const T${N} & p${N}','GiNaC::ex(p${N})');
-#define DECLARE_FUNCTION_${N}P(NAME) \\
-class NAME##_SERIAL { public: static unsigned serial; }; \\
-const unsigned NAME##_NPARAMS = ${N}; \\
-template<${SEQ1}> const GiNaC::function NAME(${SEQ2}) { \\
-       return GiNaC::function(NAME##_SERIAL::serial, ${SEQ3}); \\
-}
-
-END_OF_DECLARE_FUNCTION_MACRO
-
-$typedef_eval_funcp=generate(
-'typedef ex (* eval_funcp_${N})(${SEQ1});'."\n",
-'const ex &','','');
-
-$typedef_evalf_funcp=generate(
-'typedef ex (* evalf_funcp_${N})(${SEQ1});'."\n",
-'const ex &','','');
-
-$typedef_conjugate_funcp=generate(
-'typedef ex (* conjugate_funcp_${N})(${SEQ1});'."\n",
-'const ex &','','');
-
-$typedef_real_part_funcp=generate(
-'typedef ex (* real_part_funcp_${N})(${SEQ1});'."\n",
-'const ex &','','');
-
-$typedef_imag_part_funcp=generate(
-'typedef ex (* imag_part_funcp_${N})(${SEQ1});'."\n",
-'const ex &','','');
-
-$typedef_derivative_funcp=generate(
-'typedef ex (* derivative_funcp_${N})(${SEQ1}, unsigned);'."\n",
-'const ex &','','');
-
-$typedef_power_funcp=generate(
-'typedef ex (* power_funcp_${N})(${SEQ1}, const ex &);'."\n",
-'const ex &','','');
-
-$typedef_series_funcp=generate(
-'typedef ex (* series_funcp_${N})(${SEQ1}, const relational &, int, unsigned);'."\n",
-'const ex &','','');
-
-$typedef_print_funcp=generate(
-'typedef void (* print_funcp_${N})(${SEQ1}, const print_context &);'."\n",
-'const ex &','','');
-
-$eval_func_interface=generate('    function_options & eval_func(eval_funcp_${N} e);'."\n",'','','');
-
-$evalf_func_interface=generate('    function_options & evalf_func(evalf_funcp_${N} ef);'."\n",'','','');
-
-$conjugate_func_interface=generate('    function_options & conjugate_func(conjugate_funcp_${N} d);'."\n",'','','');
-
-$real_part_func_interface=generate('    function_options & real_part_func(real_part_funcp_${N} d);'."\n",'','','');
-
-$imag_part_func_interface=generate('    function_options & imag_part_func(imag_part_funcp_${N} d);'."\n",'','','');
-
-$derivative_func_interface=generate('    function_options & derivative_func(derivative_funcp_${N} d);'."\n",'','','');
-
-$power_func_interface=generate('    function_options & power_func(power_funcp_${N} d);'."\n",'','','');
-
-$series_func_interface=generate('    function_options & series_func(series_funcp_${N} s);'."\n",'','','');
-
-$print_func_interface=generate(
-       <<'END_OF_PRINT_FUNC_INTERFACE','','','');
-    template <class Ctx> function_options & print_func(print_funcp_${N} p)
-    {
-       test_and_set_nparams(${N});
-       set_print_func(Ctx::get_class_info_static().options.get_id(), print_funcp(p));
-       return *this;
-    }
-END_OF_PRINT_FUNC_INTERFACE
-
-$constructors_interface=generate(
-'    function(unsigned ser, ${SEQ1});'."\n",
-'const ex & param${N}','','');
-
-$constructors_implementation=generate(
-       <<'END_OF_CONSTRUCTORS_IMPLEMENTATION','const ex & param${N}','param${N}','');
-function::function(unsigned ser, ${SEQ1})
-       : exprseq(${SEQ2}), serial(ser)
-{
-}
-END_OF_CONSTRUCTORS_IMPLEMENTATION
-
-$eval_switch_statement=generate(
-       <<'END_OF_EVAL_SWITCH_STATEMENT','seq[${N}-1]','','');
-       case ${N}:
-               eval_result = ((eval_funcp_${N})(opt.eval_f))(${SEQ1});
-               break;
-END_OF_EVAL_SWITCH_STATEMENT
-
-$evalf_switch_statement=generate(
-       <<'END_OF_EVALF_SWITCH_STATEMENT','eseq[${N}-1]','','');
-       case ${N}:
-               return ((evalf_funcp_${N})(opt.evalf_f))(${SEQ1});
-END_OF_EVALF_SWITCH_STATEMENT
-
-$conjugate_switch_statement=generate(
-       <<'END_OF_DIFF_SWITCH_STATEMENT','seq[${N}-1]','','');
-       case ${N}:
-               return ((conjugate_funcp_${N})(opt.conjugate_f))(${SEQ1});
-END_OF_DIFF_SWITCH_STATEMENT
-
-$real_part_switch_statement=generate(
-       <<'END_OF_DIFF_SWITCH_STATEMENT','seq[${N}-1]','','');
-       case ${N}:
-               return ((real_part_funcp_${N})(opt.real_part_f))(${SEQ1});
-END_OF_DIFF_SWITCH_STATEMENT
-
-$imag_part_switch_statement=generate(
-       <<'END_OF_DIFF_SWITCH_STATEMENT','seq[${N}-1]','','');
-       case ${N}:
-               return ((imag_part_funcp_${N})(opt.imag_part_f))(${SEQ1});
-END_OF_DIFF_SWITCH_STATEMENT
-
-$diff_switch_statement=generate(
-       <<'END_OF_DIFF_SWITCH_STATEMENT','seq[${N}-1]','','');
-       case ${N}:
-               return ((derivative_funcp_${N})(opt.derivative_f))(${SEQ1},diff_param);
-END_OF_DIFF_SWITCH_STATEMENT
-
-$power_switch_statement=generate(
-       <<'END_OF_POWER_SWITCH_STATEMENT','seq[${N}-1]','','');
-       case ${N}:
-               return ((power_funcp_${N})(opt.power_f))(${SEQ1},power_param);
-END_OF_POWER_SWITCH_STATEMENT
-
-$series_switch_statement=generate(
-       <<'END_OF_SERIES_SWITCH_STATEMENT','seq[${N}-1]','','');
-       case ${N}:
-               try {
-                       res = ((series_funcp_${N})(opt.series_f))(${SEQ1},r,order,options);
-               } catch (do_taylor) {
-                       res = basic::series(r, order, options);
-               }
-               return res;
-END_OF_SERIES_SWITCH_STATEMENT
-
-$print_switch_statement=generate(
-       <<'END_OF_PRINT_SWITCH_STATEMENT','seq[${N}-1]','','');
-               case ${N}:
-                       ((print_funcp_${N})(pdt[id]))(${SEQ1}, c);
-                       break;
-END_OF_PRINT_SWITCH_STATEMENT
-
-$eval_func_implementation=generate(
-       <<'END_OF_EVAL_FUNC_IMPLEMENTATION','','','');
-function_options & function_options::eval_func(eval_funcp_${N} e)
-{
-       test_and_set_nparams(${N});
-       eval_f = eval_funcp(e);
-       return *this;
-}
-END_OF_EVAL_FUNC_IMPLEMENTATION
-
-$evalf_func_implementation=generate(
-       <<'END_OF_EVALF_FUNC_IMPLEMENTATION','','','');
-function_options & function_options::evalf_func(evalf_funcp_${N} ef)
-{
-       test_and_set_nparams(${N});
-       evalf_f = evalf_funcp(ef);
-       return *this;
-}
-END_OF_EVALF_FUNC_IMPLEMENTATION
-
-$conjugate_func_implementation=generate(
-       <<'END_OF_CONJUGATE_FUNC_IMPLEMENTATION','','','');
-function_options & function_options::conjugate_func(conjugate_funcp_${N} c)
-{
-       test_and_set_nparams(${N});
-       conjugate_f = conjugate_funcp(c);
-       return *this;
-}
-END_OF_CONJUGATE_FUNC_IMPLEMENTATION
-
-$real_part_func_implementation=generate(
-       <<'END_OF_REAL_PART_FUNC_IMPLEMENTATION','','','');
-function_options & function_options::real_part_func(real_part_funcp_${N} c)
-{
-       test_and_set_nparams(${N});
-       real_part_f = real_part_funcp(c);
-       return *this;
-}
-END_OF_REAL_PART_FUNC_IMPLEMENTATION
-
-$imag_part_func_implementation=generate(
-       <<'END_OF_IMAG_PART_FUNC_IMPLEMENTATION','','','');
-function_options & function_options::imag_part_func(imag_part_funcp_${N} c)
-{
-       test_and_set_nparams(${N});
-       imag_part_f = imag_part_funcp(c);
-       return *this;
-}
-END_OF_IMAG_PART_FUNC_IMPLEMENTATION
-
-$derivative_func_implementation=generate(
-       <<'END_OF_DERIVATIVE_FUNC_IMPLEMENTATION','','','');
-function_options & function_options::derivative_func(derivative_funcp_${N} d)
-{
-       test_and_set_nparams(${N});
-       derivative_f = derivative_funcp(d);
-       return *this;
-}
-END_OF_DERIVATIVE_FUNC_IMPLEMENTATION
-
-$power_func_implementation=generate(
-       <<'END_OF_POWER_FUNC_IMPLEMENTATION','','','');
-function_options & function_options::power_func(power_funcp_${N} d)
-{
-       test_and_set_nparams(${N});
-       power_f = power_funcp(d);
-       return *this;
-}
-END_OF_POWER_FUNC_IMPLEMENTATION
-
-$series_func_implementation=generate(
-       <<'END_OF_SERIES_FUNC_IMPLEMENTATION','','','');
-function_options & function_options::series_func(series_funcp_${N} s)
-{
-       test_and_set_nparams(${N});
-       series_f = series_funcp(s);
-       return *this;
-}
-END_OF_SERIES_FUNC_IMPLEMENTATION
-
-$interface=<<END_OF_INTERFACE;
-/** \@file function.h
- *
- *  Interface to class of symbolic functions. */
-
-/*
- *  This file was generated automatically by function.pl.
- *  Please do not modify it directly, edit the perl script instead!
- *  function.pl options: \$maxargs=${maxargs}
- *
- *  GiNaC Copyright (C) 1999-2011 Johannes Gutenberg University Mainz, Germany
- *
- *  This program is free software; you can redistribute it and/or modify
- *  it under the terms of the GNU General Public License as published by
- *  the Free Software Foundation; either version 2 of the License, or
- *  (at your option) any later version.
- *
- *  This program is distributed in the hope that it will be useful,
- *  but WITHOUT ANY WARRANTY; without even the implied warranty of
- *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
- *  GNU General Public License for more details.
- *
- *  You should have received a copy of the GNU General Public License
- *  along with this program; if not, write to the Free Software
- *  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
- */
-
-#ifndef GINAC_FUNCTION_H
-#define GINAC_FUNCTION_H
-
-#include "exprseq.h"
-
-// CINT needs <algorithm> to work properly with <vector>
-#include <algorithm>
-#include <string>
-#include <vector>
-
-// the following lines have been generated for max. ${maxargs} parameters
-$declare_function_macro
-// end of generated lines
-
-#define REGISTER_FUNCTION(NAME,OPT) \\
-unsigned NAME##_SERIAL::serial = \\
-       GiNaC::function::register_new(GiNaC::function_options(#NAME, NAME##_NPARAMS).OPT);
-
-namespace GiNaC {
-
-class function;
-class symmetry;
-
-typedef ex (* eval_funcp)();
-typedef ex (* evalf_funcp)();
-typedef ex (* conjugate_funcp)();
-typedef ex (* real_part_funcp)();
-typedef ex (* imag_part_funcp)();
-typedef ex (* derivative_funcp)();
-typedef ex (* power_funcp)();
-typedef ex (* series_funcp)();
-typedef void (* print_funcp)();
-
-// the following lines have been generated for max. ${maxargs} parameters
-$typedef_eval_funcp
-$typedef_evalf_funcp
-$typedef_conjugate_funcp
-$typedef_real_part_funcp
-$typedef_imag_part_funcp
-$typedef_derivative_funcp
-$typedef_power_funcp
-$typedef_series_funcp
-$typedef_print_funcp
-// end of generated lines
-
-// Alternatively, an exvector may be passed into the static function, instead
-// of individual ex objects.  Then, the number of arguments is not limited.
-typedef ex (* eval_funcp_exvector)(const exvector &);
-typedef ex (* evalf_funcp_exvector)(const exvector &);
-typedef ex (* conjugate_funcp_exvector)(const exvector &);
-typedef ex (* real_part_funcp_exvector)(const exvector &);
-typedef ex (* imag_part_funcp_exvector)(const exvector &);
-typedef ex (* derivative_funcp_exvector)(const exvector &, unsigned);
-typedef ex (* power_funcp_exvector)(const exvector &, const ex &);
-typedef ex (* series_funcp_exvector)(const exvector &, const relational &, int, unsigned);
-typedef void (* print_funcp_exvector)(const exvector &, const print_context &);
-
-
-class function_options
-{
-       friend class function;
-       friend class fderivative;
-public:
-       function_options();
-       function_options(std::string const & n, std::string const & tn=std::string());
-       function_options(std::string const & n, unsigned np);
-       ~function_options();
-       void initialize();
-
-       function_options & dummy() { return *this; }
-       function_options & set_name(std::string const & n, std::string const & tn=std::string());
-       function_options & latex_name(std::string const & tn);
-// the following lines have been generated for max. ${maxargs} parameters
-$eval_func_interface
-$evalf_func_interface
-$conjugate_func_interface
-$real_part_func_interface
-$imag_part_func_interface
-$derivative_func_interface
-$power_func_interface
-$series_func_interface
-$print_func_interface
-// end of generated lines
-       function_options & eval_func(eval_funcp_exvector e);
-       function_options & evalf_func(evalf_funcp_exvector ef);
-       function_options & conjugate_func(conjugate_funcp_exvector d);
-       function_options & real_part_func(real_part_funcp_exvector d);
-       function_options & imag_part_func(imag_part_funcp_exvector d);
-       function_options & derivative_func(derivative_funcp_exvector d);
-       function_options & power_func(power_funcp_exvector d);
-       function_options & series_func(series_funcp_exvector s);
-
-       template <class Ctx> function_options & print_func(print_funcp_exvector p)
-       {
-               print_use_exvector_args = true;
-               set_print_func(Ctx::get_class_info_static().options.get_id(), print_funcp(p));
-               return *this;
-       }
-
-       function_options & set_return_type(unsigned rt, const return_type_t* rtt = 0);
-       function_options & do_not_evalf_params();
-       function_options & remember(unsigned size, unsigned assoc_size=0,
-                                   unsigned strategy=remember_strategies::delete_never);
-       function_options & overloaded(unsigned o);
-       function_options & set_symmetry(const symmetry & s);
-
-       std::string get_name() const { return name; }
-       unsigned get_nparams() const { return nparams; }
-
-protected:
-       bool has_derivative() const { return derivative_f != NULL; }
-       bool has_power() const { return power_f != NULL; }
-       void test_and_set_nparams(unsigned n);
-       void set_print_func(unsigned id, print_funcp f);
-
-       std::string name;
-       std::string TeX_name;
-
-       unsigned nparams;
-
-       eval_funcp eval_f;
-       evalf_funcp evalf_f;
-       conjugate_funcp conjugate_f;
-       real_part_funcp real_part_f;
-       imag_part_funcp imag_part_f;
-       derivative_funcp derivative_f;
-       power_funcp power_f;
-       series_funcp series_f;
-       std::vector<print_funcp> print_dispatch_table;
-
-       bool evalf_params_first;
-
-       bool use_return_type;
-       unsigned return_type;
-       return_type_t return_type_tinfo;
-
-       bool use_remember;
-       unsigned remember_size;
-       unsigned remember_assoc_size;
-       unsigned remember_strategy;
-
-       bool eval_use_exvector_args;
-       bool evalf_use_exvector_args;
-       bool conjugate_use_exvector_args;
-       bool real_part_use_exvector_args;
-       bool imag_part_use_exvector_args;
-       bool derivative_use_exvector_args;
-       bool power_use_exvector_args;
-       bool series_use_exvector_args;
-       bool print_use_exvector_args;
-
-       unsigned functions_with_same_name;
-
-       ex symtree;
-};
-
-
-/** Exception class thrown by classes which provide their own series expansion
- *  to signal that ordinary Taylor expansion is safe. */
-class do_taylor {};
-
-
-/** The class function is used to implement builtin functions like sin, cos...
-       and user defined functions */
-class function : public exprseq
-{
-       GINAC_DECLARE_REGISTERED_CLASS(function, exprseq)
-
-       // CINT has a linking problem
-#ifndef __MAKECINT__
-       friend void ginsh_get_ginac_functions();
-#endif // def __MAKECINT__
-
-       friend class remember_table_entry;
-       // friend class remember_table_list;
-       // friend class remember_table;
-
-// member functions
-
-       // other constructors
-public:
-       function(unsigned ser);
-       // the following lines have been generated for max. ${maxargs} parameters
-$constructors_interface
-       // end of generated lines
-       function(unsigned ser, const exprseq & es);
-       function(unsigned ser, const exvector & v, bool discardable = false);
-       function(unsigned ser, std::auto_ptr<exvector> vp);
-
-       // functions overriding virtual functions from base classes
-public:
-       void print(const print_context & c, unsigned level = 0) const;
-       unsigned precedence() const {return 70;}
-       ex expand(unsigned options=0) const;
-       ex eval(int level=0) const;
-       ex evalf(int level=0) const;
-       ex eval_ncmul(const exvector & v) const;
-       unsigned calchash() const;
-       ex series(const relational & r, int order, unsigned options = 0) const;
-       ex thiscontainer(const exvector & v) const;
-       ex thiscontainer(std::auto_ptr<exvector> vp) const;
-       ex conjugate() const;
-       ex real_part() const;
-       ex imag_part() const;
-       void archive(archive_node& n) const;
-       void read_archive(const archive_node& n, lst& syms);
-protected:
-       ex derivative(const symbol & s) const;
-       bool is_equal_same_type(const basic & other) const;
-       bool match_same_type(const basic & other) const;
-       unsigned return_type() const;
-       return_type_t return_type_tinfo() const;
-       
-       // new virtual functions which can be overridden by derived classes
-       // none
-       
-       // non-virtual functions in this class
-protected:
-       ex pderivative(unsigned diff_param) const; // partial differentiation
-       static std::vector<function_options> & registered_functions();
-       bool lookup_remember_table(ex & result) const;
-       void store_remember_table(ex const & result) const;
-public:
-       ex power(const ex & exp) const;
-       static unsigned register_new(function_options const & opt);
-       static unsigned current_serial;
-       static unsigned find_function(const std::string &name, unsigned nparams);
-       unsigned get_serial() const {return serial;}
-       std::string get_name() const;
-
-// member variables
-
-protected:
-       unsigned serial;
-};
-GINAC_DECLARE_UNARCHIVER(function);
-
-// utility functions/macros
-
-template <typename T>
-inline bool is_the_function(const ex & x)
-{
-       return is_exactly_a<function>(x)
-           && ex_to<function>(x).get_serial() == T::serial;
-}
-
-// Check whether OBJ is the specified symbolic function.
-#define is_ex_the_function(OBJ, FUNCNAME) (GiNaC::is_the_function<FUNCNAME##_SERIAL>(OBJ))
-
-} // namespace GiNaC
-
-#endif // ndef GINAC_FUNCTION_H
-
-END_OF_INTERFACE
-
-$implementation=<<END_OF_IMPLEMENTATION;
-/** \@file function.cpp
- *
- *  Implementation of class of symbolic functions. */
-
-/*
- *  This file was generated automatically by function.pl.
- *  Please do not modify it directly, edit the perl script instead!
- *  function.pl options: \$maxargs=${maxargs}
- *
- *  GiNaC Copyright (C) 1999-2011 Johannes Gutenberg University Mainz, Germany
- *
- *  This program is free software; you can redistribute it and/or modify
- *  it under the terms of the GNU General Public License as published by
- *  the Free Software Foundation; either version 2 of the License, or
- *  (at your option) any later version.
- *
- *  This program is distributed in the hope that it will be useful,
- *  but WITHOUT ANY WARRANTY; without even the implied warranty of
- *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
- *  GNU General Public License for more details.
- *
- *  You should have received a copy of the GNU General Public License
- *  along with this program; if not, write to the Free Software
- *  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
- */
-
-#include "function.h"
-#include "operators.h"
-#include "fderivative.h"
-#include "ex.h"
-#include "lst.h"
-#include "symmetry.h"
-#include "print.h"
-#include "power.h"
-#include "archive.h"
-#include "inifcns.h"
-#include "tostring.h"
-#include "utils.h"
-#include "hash_seed.h"
-#include "remember.h"
-
-#include <iostream>
-#include <limits>
-#include <list>
-#include <stdexcept>
-#include <string>
-
-namespace GiNaC {
-
-//////////
-// helper class function_options
-//////////
-
-function_options::function_options()
-{
-       initialize();
-}
-
-function_options::function_options(std::string const & n, std::string const & tn)
-{
-       initialize();
-       set_name(n, tn);
-}
-
-function_options::function_options(std::string const & n, unsigned np)
-{
-       initialize();
-       set_name(n, std::string());
-       nparams = np;
-}
-
-function_options::~function_options()
-{
-       // nothing to clean up at the moment
-}
-
-void function_options::initialize()
-{
-       set_name("unnamed_function", "\\\\mbox{unnamed}");
-       nparams = 0;
-       eval_f = evalf_f = real_part_f = imag_part_f = conjugate_f = derivative_f
-               = power_f = series_f = 0;
-       evalf_params_first = true;
-       use_return_type = false;
-       eval_use_exvector_args = false;
-       evalf_use_exvector_args = false;
-       conjugate_use_exvector_args = false;
-       real_part_use_exvector_args = false;
-       imag_part_use_exvector_args = false;
-       derivative_use_exvector_args = false;
-       power_use_exvector_args = false;
-       series_use_exvector_args = false;
-       print_use_exvector_args = false;
-       use_remember = false;
-       functions_with_same_name = 1;
-       symtree = 0;
-}
-
-function_options & function_options::set_name(std::string const & n,
-                                              std::string const & tn)
-{
-       name = n;
-       if (tn==std::string())
-               TeX_name = "\\\\mbox{"+name+"}";
-       else
-               TeX_name = tn;
-       return *this;
-}
-
-function_options & function_options::latex_name(std::string const & tn)
-{
-       TeX_name = tn;
-       return *this;
-}
-
-// the following lines have been generated for max. ${maxargs} parameters
-$eval_func_implementation
-$evalf_func_implementation
-$conjugate_func_implementation
-$real_part_func_implementation
-$imag_part_func_implementation
-$derivative_func_implementation
-$power_func_implementation
-$series_func_implementation
-// end of generated lines
-
-function_options& function_options::eval_func(eval_funcp_exvector e)
-{
-       eval_use_exvector_args = true;
-       eval_f = eval_funcp(e);
-       return *this;
-}
-function_options& function_options::evalf_func(evalf_funcp_exvector ef)
-{
-       evalf_use_exvector_args = true;
-       evalf_f = evalf_funcp(ef);
-       return *this;
-}
-function_options& function_options::conjugate_func(conjugate_funcp_exvector c)
-{
-       conjugate_use_exvector_args = true;
-       conjugate_f = conjugate_funcp(c);
-       return *this;
-}
-function_options& function_options::real_part_func(real_part_funcp_exvector c)
-{
-       real_part_use_exvector_args = true;
-       real_part_f = real_part_funcp(c);
-       return *this;
-}
-function_options& function_options::imag_part_func(imag_part_funcp_exvector c)
-{
-       imag_part_use_exvector_args = true;
-       imag_part_f = imag_part_funcp(c);
-       return *this;
-}
-
-function_options& function_options::derivative_func(derivative_funcp_exvector d)
-{
-       derivative_use_exvector_args = true;
-       derivative_f = derivative_funcp(d);
-       return *this;
-}
-function_options& function_options::power_func(power_funcp_exvector d)
-{
-       power_use_exvector_args = true;
-       power_f = power_funcp(d);
-       return *this;
-}
-function_options& function_options::series_func(series_funcp_exvector s)
-{
-       series_use_exvector_args = true;
-       series_f = series_funcp(s);
-       return *this;
-}
-
-function_options & function_options::set_return_type(unsigned rt, const return_type_t* rtt)
-{
-       use_return_type = true;
-       return_type = rt;
-       if (rtt != 0)
-               return_type_tinfo = *rtt;
-       else
-               return_type_tinfo = make_return_type_t<function>();
-       return *this;
-}
-
-function_options & function_options::do_not_evalf_params()
-{
-       evalf_params_first = false;
-       return *this;
-}
-
-function_options & function_options::remember(unsigned size,
-                                              unsigned assoc_size,
-                                              unsigned strategy)
-{
-       use_remember = true;
-       remember_size = size;
-       remember_assoc_size = assoc_size;
-       remember_strategy = strategy;
-       return *this;
-}
-
-function_options & function_options::overloaded(unsigned o)
-{
-       functions_with_same_name = o;
-       return *this;
-}
-
-function_options & function_options::set_symmetry(const symmetry & s)
-{
-       symtree = s;
-       return *this;
-}
-       
-void function_options::test_and_set_nparams(unsigned n)
-{
-       if (nparams==0) {
-               nparams = n;
-       } else if (nparams!=n) {
-               // we do not throw an exception here because this code is
-               // usually executed before main(), so the exception could not
-               // be caught anyhow
-               std::cerr << "WARNING: " << name << "(): number of parameters ("
-                         << n << ") differs from number set before (" 
-                         << nparams << ")" << std::endl;
-       }
-}
-
-void function_options::set_print_func(unsigned id, print_funcp f)
-{
-       if (id >= print_dispatch_table.size())
-               print_dispatch_table.resize(id + 1);
-       print_dispatch_table[id] = f;
-}
-
-/** This can be used as a hook for external applications. */
-unsigned function::current_serial = 0;
-
-
-GINAC_IMPLEMENT_REGISTERED_CLASS(function, exprseq)
-
-//////////
-// default constructor
-//////////
-
-// public
-
-function::function() : serial(0)
-{
-}
-
-//////////
-// other constructors
-//////////
-
-// public
-
-function::function(unsigned ser) : serial(ser)
-{
-}
-
-// the following lines have been generated for max. ${maxargs} parameters
-$constructors_implementation
-// end of generated lines
-
-function::function(unsigned ser, const exprseq & es) : exprseq(es), serial(ser)
-{
-
-       // Force re-evaluation even if the exprseq was already evaluated
-       // (the exprseq copy constructor copies the flags)
-       clearflag(status_flags::evaluated);
-}
-
-function::function(unsigned ser, const exvector & v, bool discardable) 
-  : exprseq(v,discardable), serial(ser)
-{
-       if ( ser >= registered_functions().size() ) {
-               throw std::runtime_error("function does not exist");
-       }
-}
-
-function::function(unsigned ser, std::auto_ptr<exvector> vp) 
-  : exprseq(vp), serial(ser)
-{
-}
-
-//////////
-// archiving
-//////////
-
-/** Construct object from archive_node. */
-void function::read_archive(const archive_node& n, lst& sym_lst)
-{
-       inherited::read_archive(n, sym_lst);
-       // Find serial number by function name
-       std::string s;
-       if (n.find_string("name", s)) {
-               unsigned int ser = 0;
-               std::vector<function_options>::const_iterator i = registered_functions().begin(), iend = registered_functions().end();
-               while (i != iend) {
-                       if (s == i->name) {
-                               serial = ser;
-                               return;
-                       }
-                       ++i; ++ser;
-               }
-               throw (std::runtime_error("unknown function '" + s + "' in archive"));
-       } else
-               throw (std::runtime_error("unnamed function in archive"));
-}
-
-/** Archive the object. */
-void function::archive(archive_node &n) const
-{
-       inherited::archive(n);
-       GINAC_ASSERT(serial < registered_functions().size());
-       n.add_string("name", registered_functions()[serial].name);
-}
-
-GINAC_BIND_UNARCHIVER(function);
-
-//////////
-// functions overriding virtual functions from base classes
-//////////
-
-// public
-
-void function::print(const print_context & c, unsigned level) const
-{
-       GINAC_ASSERT(serial<registered_functions().size());
-       const function_options &opt = registered_functions()[serial];
-       const std::vector<print_funcp> &pdt = opt.print_dispatch_table;
-
-       // Dynamically dispatch on print_context type
-       const print_context_class_info *pc_info = &c.get_class_info();
-
-next_context:
-       unsigned id = pc_info->options.get_id();
-       if (id >= pdt.size() || pdt[id] == NULL) {
-
-               // Method not found, try parent print_context class
-               const print_context_class_info *parent_pc_info = pc_info->get_parent();
-               if (parent_pc_info) {
-                       pc_info = parent_pc_info;
-                       goto next_context;
-               }
-
-               // Method still not found, use default output
-               if (is_a<print_tree>(c)) {
-
-                       c.s << std::string(level, ' ') << class_name() << " "
-                           << opt.name << " @" << this
-                           << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
-                           << ", nops=" << nops()
-                           << std::endl;
-                       unsigned delta_indent = static_cast<const print_tree &>(c).delta_indent;
-                       for (size_t i=0; i<seq.size(); ++i)
-                               seq[i].print(c, level + delta_indent);
-                       c.s << std::string(level + delta_indent, ' ') << "=====" << std::endl;
-
-               } else if (is_a<print_csrc>(c)) {
-
-                       // Print function name in lowercase
-                       std::string lname = opt.name;
-                       size_t num = lname.size();
-                       for (size_t i=0; i<num; i++)
-                               lname[i] = tolower(lname[i]);
-                       c.s << lname;
-                       printseq(c, '(', ',', ')', exprseq::precedence(), function::precedence());
-
-               } else if (is_a<print_latex>(c)) {
-                       c.s << opt.TeX_name;
-                       printseq(c, '(', ',', ')', exprseq::precedence(), function::precedence());
-               } else {
-                       c.s << opt.name;
-                       printseq(c, '(', ',', ')', exprseq::precedence(), function::precedence());
-               }
-
-       } else {
-
-               // Method found, call it
-               current_serial = serial;
-               if (opt.print_use_exvector_args)
-                       ((print_funcp_exvector)pdt[id])(seq, c);
-               else switch (opt.nparams) {
-                       // the following lines have been generated for max. ${maxargs} parameters
-${print_switch_statement}
-                       // end of generated lines
-               default:
-                       throw(std::logic_error("function::print(): invalid nparams"));
-               }
-       }
-}
-
-ex function::expand(unsigned options) const
-{
-       // Only expand arguments when asked to do so
-       if (options & expand_options::expand_function_args)
-               return inherited::expand(options);
-       else
-               return (options == 0) ? setflag(status_flags::expanded) : *this;
-}
-
-ex function::eval(int level) const
-{
-       if (level>1) {
-               // first evaluate children, then we will end up here again
-               return function(serial,evalchildren(level));
-       }
-
-       GINAC_ASSERT(serial<registered_functions().size());
-       const function_options &opt = registered_functions()[serial];
-
-       // Canonicalize argument order according to the symmetry properties
-       if (seq.size() > 1 && !(opt.symtree.is_zero())) {
-               exvector v = seq;
-               GINAC_ASSERT(is_a<symmetry>(opt.symtree));
-               int sig = canonicalize(v.begin(), ex_to<symmetry>(opt.symtree));
-               if (sig != std::numeric_limits<int>::max()) {
-                       // Something has changed while sorting arguments, more evaluations later
-                       if (sig == 0)
-                               return _ex0;
-                       return ex(sig) * thiscontainer(v);
-               }
-       }
-
-       if (opt.eval_f==0) {
-               return this->hold();
-       }
-
-       bool use_remember = opt.use_remember;
-       ex eval_result;
-       if (use_remember && lookup_remember_table(eval_result)) {
-               return eval_result;
-       }
-       current_serial = serial;
-       if (opt.eval_use_exvector_args)
-               eval_result = ((eval_funcp_exvector)(opt.eval_f))(seq);
-       else
-       switch (opt.nparams) {
-               // the following lines have been generated for max. ${maxargs} parameters
-${eval_switch_statement}
-               // end of generated lines
-       default:
-               throw(std::logic_error("function::eval(): invalid nparams"));
-       }
-       if (use_remember) {
-               store_remember_table(eval_result);
-       }
-       return eval_result;
-}
-
-ex function::evalf(int level) const
-{
-       GINAC_ASSERT(serial<registered_functions().size());
-       const function_options &opt = registered_functions()[serial];
-
-       // Evaluate children first
-       exvector eseq;
-       if (level == 1 || !(opt.evalf_params_first))
-               eseq = seq;
-       else if (level == -max_recursion_level)
-               throw(std::runtime_error("max recursion level reached"));
-       else {
-               eseq.reserve(seq.size());
-               --level;
-               exvector::const_iterator it = seq.begin(), itend = seq.end();
-               while (it != itend) {
-                       eseq.push_back(it->evalf(level));
-                       ++it;
-               }
-       }
-
-       if (opt.evalf_f==0) {
-               return function(serial,eseq).hold();
-       }
-       current_serial = serial;
-       if (opt.evalf_use_exvector_args)
-               return ((evalf_funcp_exvector)(opt.evalf_f))(seq);
-       switch (opt.nparams) {
-               // the following lines have been generated for max. ${maxargs} parameters
-${evalf_switch_statement}
-               // end of generated lines
-       }
-       throw(std::logic_error("function::evalf(): invalid nparams"));
-}
-
-/**
- *  This method is defined to be in line with behaviour of function::return_type()
- */
-ex function::eval_ncmul(const exvector & v) const
-{
-       // If this function is called then the list of arguments is non-empty
-       // and the first argument is non-commutative, see  function::return_type()
-       return seq.begin()->eval_ncmul(v);
-}
-
-unsigned function::calchash() const
-{
-       unsigned v = golden_ratio_hash(make_hash_seed(typeid(*this)) ^ serial);
-       for (size_t i=0; i<nops(); i++) {
-               v = rotate_left(v);
-               v ^= this->op(i).gethash();
-       }
-
-       if (flags & status_flags::evaluated) {
-               setflag(status_flags::hash_calculated);
-               hashvalue = v;
-       }
-       return v;
-}
-
-ex function::thiscontainer(const exvector & v) const
-{
-       return function(serial, v);
-}
-
-ex function::thiscontainer(std::auto_ptr<exvector> vp) const
-{
-       return function(serial, vp);
-}
-
-/** Implementation of ex::series for functions.
- *  \@see ex::series */
-ex function::series(const relational & r, int order, unsigned options) const
-{
-       GINAC_ASSERT(serial<registered_functions().size());
-       const function_options &opt = registered_functions()[serial];
-
-       if (opt.series_f==0) {
-               return basic::series(r, order);
-       }
-       ex res;
-       current_serial = serial;
-       if (opt.series_use_exvector_args) {
-               try {
-                       res = ((series_funcp_exvector)(opt.series_f))(seq, r, order, options);
-               } catch (do_taylor) {
-                       res = basic::series(r, order, options);
-               }
-               return res;
-       }
-       switch (opt.nparams) {
-               // the following lines have been generated for max. ${maxargs} parameters
-${series_switch_statement}
-               // end of generated lines
-       }
-       throw(std::logic_error("function::series(): invalid nparams"));
-}
-
-/** Implementation of ex::conjugate for functions. */
-ex function::conjugate() const
-{
-       GINAC_ASSERT(serial<registered_functions().size());
-       const function_options & opt = registered_functions()[serial];
-
-       if (opt.conjugate_f==0) {
-               return conjugate_function(*this).hold();
-       }
-
-       if (opt.conjugate_use_exvector_args) {
-               return ((conjugate_funcp_exvector)(opt.conjugate_f))(seq);
-       }
-
-       switch (opt.nparams) {
-               // the following lines have been generated for max. ${maxargs} parameters
-${conjugate_switch_statement}
-               // end of generated lines
-       }
-       throw(std::logic_error("function::conjugate(): invalid nparams"));
-}
-
-/** Implementation of ex::real_part for functions. */
-ex function::real_part() const
-{
-       GINAC_ASSERT(serial<registered_functions().size());
-       const function_options & opt = registered_functions()[serial];
-
-       if (opt.real_part_f==0)
-               return basic::real_part();
-
-       if (opt.real_part_use_exvector_args)
-               return ((real_part_funcp_exvector)(opt.real_part_f))(seq);
-
-       switch (opt.nparams) {
-               // the following lines have been generated for max. ${maxargs} parameters
-${real_part_switch_statement}
-               // end of generated lines
-       }
-       throw(std::logic_error("function::real_part(): invalid nparams"));
-}
-
-/** Implementation of ex::imag_part for functions. */
-ex function::imag_part() const
-{
-       GINAC_ASSERT(serial<registered_functions().size());
-       const function_options & opt = registered_functions()[serial];
-
-       if (opt.imag_part_f==0)
-               return basic::imag_part();
-
-       if (opt.imag_part_use_exvector_args)
-               return ((imag_part_funcp_exvector)(opt.imag_part_f))(seq);
-
-       switch (opt.nparams) {
-               // the following lines have been generated for max. ${maxargs} parameters
-${imag_part_switch_statement}
-               // end of generated lines
-       }
-       throw(std::logic_error("function::imag_part(): invalid nparams"));
-}
-
-// protected
-
-/** Implementation of ex::diff() for functions. It applies the chain rule,
- *  except for the Order term function.
- *  \@see ex::diff */
-ex function::derivative(const symbol & s) const
-{
-       ex result;
-
-       if (serial == Order_SERIAL::serial) {
-               // Order Term function only differentiates the argument
-               return Order(seq[0].diff(s));
-       } else {
-               // Chain rule
-               ex arg_diff;
-               size_t num = seq.size();
-               for (size_t i=0; i<num; i++) {
-                       arg_diff = seq[i].diff(s);
-                       // We apply the chain rule only when it makes sense.  This is not
-                       // just for performance reasons but also to allow functions to
-                       // throw when differentiated with respect to one of its arguments
-                       // without running into trouble with our automatic full
-                       // differentiation:
-                       if (!arg_diff.is_zero())
-                               result += pderivative(i)*arg_diff;
-               }
-       }
-       return result;
-}
-
-int function::compare_same_type(const basic & other) const
-{
-       GINAC_ASSERT(is_a<function>(other));
-       const function & o = static_cast<const function &>(other);
-
-       if (serial != o.serial)
-               return serial < o.serial ? -1 : 1;
-       else
-               return exprseq::compare_same_type(o);
-}
-
-bool function::is_equal_same_type(const basic & other) const
-{
-       GINAC_ASSERT(is_a<function>(other));
-       const function & o = static_cast<const function &>(other);
-
-       if (serial != o.serial)
-               return false;
-       else
-               return exprseq::is_equal_same_type(o);
-}
-
-bool function::match_same_type(const basic & other) const
-{
-       GINAC_ASSERT(is_a<function>(other));
-       const function & o = static_cast<const function &>(other);
-
-       return serial == o.serial;
-}
-
-unsigned function::return_type() const
-{
-       GINAC_ASSERT(serial<registered_functions().size());
-       const function_options &opt = registered_functions()[serial];
-
-       if (opt.use_return_type) {
-               // Return type was explicitly specified
-               return opt.return_type;
-       } else {
-               // Default behavior is to use the return type of the first
-               // argument. Thus, exp() of a matrix behaves like a matrix, etc.
-               if (seq.empty())
-                       return return_types::commutative;
-               else
-                       return seq.begin()->return_type();
-       }
-}
-
-return_type_t function::return_type_tinfo() const
-{
-       GINAC_ASSERT(serial<registered_functions().size());
-       const function_options &opt = registered_functions()[serial];
-
-       if (opt.use_return_type) {
-               // Return type was explicitly specified
-               return opt.return_type_tinfo;
-       } else {
-               // Default behavior is to use the return type of the first
-               // argument. Thus, exp() of a matrix behaves like a matrix, etc.
-               if (seq.empty())
-                       return make_return_type_t<function>();
-               else
-                       return seq.begin()->return_type_tinfo();
-       }
-}
-
-//////////
-// new virtual functions which can be overridden by derived classes
-//////////
-
-// none
-
-//////////
-// non-virtual functions in this class
-//////////
-
-// protected
-
-ex function::pderivative(unsigned diff_param) const // partial differentiation
-{
-       GINAC_ASSERT(serial<registered_functions().size());
-       const function_options &opt = registered_functions()[serial];
-       
-       // No derivative defined? Then return abstract derivative object
-       if (opt.derivative_f == NULL)
-               return fderivative(serial, diff_param, seq);
-
-       current_serial = serial;
-       if (opt.derivative_use_exvector_args)
-               return ((derivative_funcp_exvector)(opt.derivative_f))(seq, diff_param);
-       switch (opt.nparams) {
-               // the following lines have been generated for max. ${maxargs} parameters
-${diff_switch_statement}
-               // end of generated lines
-       }
-       throw(std::logic_error("function::pderivative(): no diff function defined"));
-}
-
-ex function::power(const ex & power_param) const // power of function
-{
-       GINAC_ASSERT(serial<registered_functions().size());
-       const function_options &opt = registered_functions()[serial];
-       
-       // No derivative defined? Then return abstract derivative object
-       if (opt.power_f == NULL)
-               return (new GiNaC::power(*this, power_param))->setflag(status_flags::dynallocated |
-                                                                      status_flags::evaluated);
-
-       current_serial = serial;
-       if (opt.power_use_exvector_args)
-               return ((power_funcp_exvector)(opt.power_f))(seq,  power_param);
-       switch (opt.nparams) {
-               // the following lines have been generated for max. ${maxargs} parameters
-${power_switch_statement}
-               // end of generated lines
-       }
-       throw(std::logic_error("function::power(): no power function defined"));
-}
-
-std::vector<function_options> & function::registered_functions()
-{
-       static std::vector<function_options> rf = std::vector<function_options>();
-       return rf;
-}
-
-bool function::lookup_remember_table(ex & result) const
-{
-       return remember_table::remember_tables()[this->serial].lookup_entry(*this,result);
-}
-
-void function::store_remember_table(ex const & result) const
-{
-       remember_table::remember_tables()[this->serial].add_entry(*this,result);
-}
-
-// public
-
-unsigned function::register_new(function_options const & opt)
-{
-       size_t same_name = 0;
-       for (size_t i=0; i<registered_functions().size(); ++i) {
-               if (registered_functions()[i].name==opt.name) {
-                       ++same_name;
-               }
-       }
-       if (same_name>=opt.functions_with_same_name) {
-               // we do not throw an exception here because this code is
-               // usually executed before main(), so the exception could not
-               // caught anyhow
-               std::cerr << "WARNING: function name " << opt.name
-                         << " already in use!" << std::endl;
-       }
-       registered_functions().push_back(opt);
-       if (opt.use_remember) {
-               remember_table::remember_tables().
-                       push_back(remember_table(opt.remember_size,
-                                                opt.remember_assoc_size,
-                                                opt.remember_strategy));
-       } else {
-               remember_table::remember_tables().push_back(remember_table());
-       }
-       return registered_functions().size()-1;
-}
-
-/** Find serial number of function by name and number of parameters.
- *  Throws exception if function was not found. */
-unsigned function::find_function(const std::string &name, unsigned nparams)
-{
-       std::vector<function_options>::const_iterator i = function::registered_functions().begin(), end = function::registered_functions().end();
-       unsigned serial = 0;
-       while (i != end) {
-               if (i->get_name() == name && i->get_nparams() == nparams)
-                       return serial;
-               ++i;
-               ++serial;
-       }
-       throw (std::runtime_error("no function '" + name + "' with " + ToString(nparams) + " parameters defined"));
-}
-
-/** Return the print name of the function. */
-std::string function::get_name() const
-{
-       if ( serial >= registered_functions().size() ) {
-               throw std::runtime_error("unknown function");
-       }
-       return registered_functions()[serial].name;
-}
-
-} // namespace GiNaC
-
-END_OF_IMPLEMENTATION
-
-print "Creating interface file function.h...";
-open OUT,">function.h" or die "cannot open function.h";
-print OUT $interface;
-close OUT;
-print "ok.\n";
-
-print "Creating implementation file function.cpp...";
-open OUT,">function.cpp" or die "cannot open function.cpp";
-print OUT $implementation;
-close OUT;
-print "ok.\n";
-
-print "done.\n";
diff --git a/ginac/function.py b/ginac/function.py
new file mode 100755 (executable)
index 0000000..6ceb254
--- /dev/null
@@ -0,0 +1,35 @@
+#!/usr/bin/env python
+# encoding: utf-8
+
+maxargs = 14
+methods = "eval evalf conjugate real_part imag_part derivative power series print".split()
+
+import sys, os, optparse
+sys.path.insert(0, os.path.join(os.path.dirname(__file__), '..', 'scripts'))
+import yaptu
+
+def seq(template, N, start = 1, separator = ', '):
+       return separator.join([ template % { 'n' : n } for n in range(start, N + start) ])
+
+def main():
+       parser = optparse.OptionParser()
+       parser.add_option("-o", dest="outfile")
+       options, args = parser.parse_args()
+       cop = yaptu.copier(globals())
+       if not options.outfile is None:
+               cop.ouf = open(options.outfile, 'wt')
+       inp = sys.stdin
+       if len(args) >= 1:
+               inp = open(args[0])
+       cop.copy(inp)
+       if inp != sys.stdin:
+               inp.close()
+       if cop.ouf != sys.stdout:
+               cop.ouf.flush()
+               cop.ouf.close()
+       return 0
+
+if __name__== '__main__':
+       ret = main()
+       sys.exit(ret)
+
index ab300a4..ead4f1f 100644 (file)
@@ -732,9 +732,10 @@ static ex f_ginac_function(const exprseq &es, int serial)
 
 // All registered GiNaC functions
 namespace GiNaC {
-void ginsh_get_ginac_functions(void)
+static void ginsh_get_ginac_functions(void)
 {
-       vector<function_options>::const_iterator i = function::registered_functions().begin(), end = function::registered_functions().end();
+       vector<function_options> gfv = function::get_registered_functions();
+       vector<function_options>::const_iterator i = gfv.begin(), end = gfv.end();
        unsigned serial = 0;
        while (i != end) {
                fcns.insert(make_pair(i->get_name(), fcn_desc(f_ginac_function, i->get_nparams(), serial)));
diff --git a/scripts/yaptu.py b/scripts/yaptu.py
new file mode 100644 (file)
index 0000000..ddf18f5
--- /dev/null
@@ -0,0 +1,93 @@
+#!/usr/bin/env python
+"""
+Yet Another Python Templating Utility, Version 1.2, by Alex Martelli.
+Distributed under PSF license (http://docs.python.org/license.html).
+"""
+
+import re
+import sys
+
+# utility stuff to avoid tests in the mainline code
+class _nevermatch:
+    "Polymorphic with a regex that never matches"
+    def match(self, line):
+        return None
+_never = _nevermatch()     # one reusable instance of it suffices
+def identity(string, why):
+    "A do-nothing-special-to-the-input, just-return-it function"
+    return string
+def nohandle(string):
+    "A do-nothing handler that just re-raises the exception"
+    raise
+
+_default_rex = re.compile('@([^@]+)@')
+_default_rbe = re.compile('\+\+\+')
+_default_ren = re.compile('---')
+_default_rco = re.compile('===')
+
+# and now the real thing
+class copier:
+    "Smart-copier (YAPTU) class"
+    def copyblock(self, i=0, last=None):
+        "Main copy method: process lines [i,last) of block"
+        def repl(match, self=self):
+            "return the eval of a found expression, for replacement"
+            # uncomment for debug:
+           # print '!!! replacing',match.group(1)
+            expr = self.preproc(match.group(1), 'eval')
+            try: return str(eval(expr, self.globals, self.locals))
+            except: return str(self.handle(expr))
+        block = self.locals['_bl']
+        if last is None: last = len(block)
+        while i<last:
+            line = block[i]
+            match = self.restat.match(line)
+            if match:   # a statement starts "here" (at line block[i])
+                # i is the last line to _not_ process
+                stat = match.string[match.end(0):].strip()
+                j=i+1   # look for 'finish' from here onwards
+                nest=1  # count nesting levels of statements
+                while j<last:
+                    line = block[j]
+                    # first look for nested statements or 'finish' lines
+                    if self.restend.match(line):    # found a statement-end
+                        nest = nest - 1     # update (decrease) nesting
+                        if nest==0: break   # j is first line to _not_ process
+                    elif self.restat.match(line):   # found a nested statement
+                        nest = nest + 1     # update (increase) nesting
+                    elif nest==1:   # look for continuation only at this nesting
+                        match = self.recont.match(line)
+                        if match:                   # found a contin.-statement
+                            nestat = match.string[match.end(0):].strip()
+                            stat = '%s _cb(%s,%s)\n%s' % (stat,i+1,j,nestat)
+                            i=j     # again, i is the last line to _not_ process
+                    j=j+1
+                stat = self.preproc(stat, 'exec')
+                stat = '%s _cb(%s,%s)' % (stat,i+1,j)
+                # for debugging, uncomment...:
+               # print "-> Executing: {"+stat+"}"
+                exec stat in self.globals,self.locals
+                i=j+1
+            else:       # normal line, just copy with substitution
+                self.ouf.write(self.regex.sub(repl,line))
+                i=i+1
+    def __init__(self, dict={}, regex=_default_rex,
+            restat=_default_rbe, restend=_default_ren, recont=_default_rco,
+            preproc=identity, handle=nohandle, ouf=sys.stdout):
+        "Initialize self's attributes"
+        self.regex   = regex
+        self.globals = dict
+        self.locals  = { '_cb':self.copyblock }
+        self.restat  = restat
+        self.restend = restend
+        self.recont  = recont
+        self.preproc = preproc
+        self.handle  = handle
+        self.ouf     = ouf
+    def copy(self, inf=sys.stdin, block=None):
+        "Entry point: copy-with-processing a file, or a block of lines"
+        if block is None: block = inf.readlines()
+        self.locals['_bl'] = block
+        self.copyblock()
+
+