- Pearu Peterson's patch for class function giving them better support
[ginac.git] / ginac / function.pl
index b0564e6e45f105422029acccdf6c108a95323979..68673ddc38e9fb0032eefa1fb733a17f6f623201 100755 (executable)
@@ -15,79 +15,68 @@ sub generate_seq {
 }
 
 sub generate_from_to {
-       my ($template,$seq_template1,$seq_template2,$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,$seq_template2)=@_;
-       return generate_from_to($template,$seq_template1,$seq_template2,1,$maxargs);
+       my ($template,$seq_template1,$seq_template2,$seq_template3)=@_;
+       return generate_from_to($template,$seq_template1,$seq_template2,$seq_template3,1,$maxargs);
 }
 
-$declare_function_macro = <<'END_OF_DECLARE_FUNCTION_1_AND_2P_MACRO';
-#define DECLARE_FUNCTION_1P(NAME) \
-extern const unsigned function_index_##NAME; \
-inline GiNaC::function NAME(const GiNaC::ex & p1) { \
-       return GiNaC::function(function_index_##NAME, p1); \
-}
-#define DECLARE_FUNCTION_2P(NAME) \
-extern const unsigned function_index_##NAME; \
-inline GiNaC::function NAME(const GiNaC::ex & p1, const GiNaC::ex & p2) { \
-       return GiNaC::function(function_index_##NAME, p1, p2); \
-}
-
-END_OF_DECLARE_FUNCTION_1_AND_2P_MACRO
-
-$declare_function_macro .= generate_from_to(
-       <<'END_OF_DECLARE_FUNCTION_MACRO','const GiNaC::ex & p${N}','p${N}',3,$maxargs);
+$declare_function_macro = generate(
+       <<'END_OF_DECLARE_FUNCTION_MACRO','typename T${N}','const T${N} & p${N}','GiNaC::ex(p${N})');
 #define DECLARE_FUNCTION_${N}P(NAME) \\
 extern const unsigned function_index_##NAME; \\
-inline GiNaC::function NAME(${SEQ1}) { \\
-       return GiNaC::function(function_index_##NAME, ${SEQ2}); \\
+template<${SEQ1}> \\
+inline const GiNaC::function NAME(${SEQ2}) { \\
+       return GiNaC::function(function_index_##NAME, ${SEQ3}); \\
 }
 
 END_OF_DECLARE_FUNCTION_MACRO
 
 $typedef_eval_funcp=generate(
 'typedef ex (* eval_funcp_${N})(${SEQ1});'."\n",
-'const ex &','');
+'const ex &','','');
 
 $typedef_evalf_funcp=generate(
 'typedef ex (* evalf_funcp_${N})(${SEQ1});'."\n",
-'const ex &','');
+'const ex &','','');
 
 $typedef_derivative_funcp=generate(
 'typedef ex (* derivative_funcp_${N})(${SEQ1}, unsigned);'."\n",
-'const ex &','');
+'const ex &','','');
 
 $typedef_series_funcp=generate(
 'typedef ex (* series_funcp_${N})(${SEQ1}, const relational &, int, unsigned);'."\n",
-'const ex &','');
+'const ex &','','');
 
-$eval_func_interface=generate('    function_options & eval_func(eval_funcp_${N} e);'."\n",'','');
+$eval_func_interface=generate('    function_options & eval_func(eval_funcp_${N} e);'."\n",'','','');
 
-$evalf_func_interface=generate('    function_options & evalf_func(evalf_funcp_${N} ef);'."\n",'','');
+$evalf_func_interface=generate('    function_options & evalf_func(evalf_funcp_${N} ef);'."\n",'','','');
 
-$derivative_func_interface=generate('    function_options & derivative_func(derivative_funcp_${N} d);'."\n",'','');
+$derivative_func_interface=generate('    function_options & derivative_func(derivative_funcp_${N} d);'."\n",'','','');
 
-$series_func_interface=generate('    function_options & series_func(series_funcp_${N} s);'."\n",'','');
+$series_func_interface=generate('    function_options & series_func(series_funcp_${N} s);'."\n",'','','');
 
 $constructors_interface=generate(
 '    function(unsigned ser, ${SEQ1});'."\n",
-'const ex & param${N}','');
+'const ex & param${N}','','');
 
 $constructors_implementation=generate(
-       <<'END_OF_CONSTRUCTORS_IMPLEMENTATION','const ex & param${N}','param${N}');
+       <<'END_OF_CONSTRUCTORS_IMPLEMENTATION','const ex & param${N}','param${N}','');
 function::function(unsigned ser, ${SEQ1})
        : exprseq(${SEQ2}), serial(ser)
 {
@@ -97,26 +86,26 @@ function::function(unsigned ser, ${SEQ1})
 END_OF_CONSTRUCTORS_IMPLEMENTATION
 
 $eval_switch_statement=generate(
-       <<'END_OF_EVAL_SWITCH_STATEMENT','seq[${N}-1]','');
+       <<'END_OF_EVAL_SWITCH_STATEMENT','seq[${N}-1]','','');
        case ${N}:
-               eval_result=((eval_funcp_${N})(registered_functions()[serial].eval_f))(${SEQ1});
+               eval_result = ((eval_funcp_${N})(registered_functions()[serial].eval_f))(${SEQ1});
                break;
 END_OF_EVAL_SWITCH_STATEMENT
 
 $evalf_switch_statement=generate(
-       <<'END_OF_EVALF_SWITCH_STATEMENT','eseq[${N}-1]','');
+       <<'END_OF_EVALF_SWITCH_STATEMENT','eseq[${N}-1]','','');
        case ${N}:
                return ((evalf_funcp_${N})(registered_functions()[serial].evalf_f))(${SEQ1});
 END_OF_EVALF_SWITCH_STATEMENT
 
 $diff_switch_statement=generate(
-       <<'END_OF_DIFF_SWITCH_STATEMENT','seq[${N}-1]','');
+       <<'END_OF_DIFF_SWITCH_STATEMENT','seq[${N}-1]','','');
        case ${N}:
                return ((derivative_funcp_${N})(registered_functions()[serial].derivative_f))(${SEQ1},diff_param);
 END_OF_DIFF_SWITCH_STATEMENT
 
 $series_switch_statement=generate(
-       <<'END_OF_SERIES_SWITCH_STATEMENT','seq[${N}-1]','');
+       <<'END_OF_SERIES_SWITCH_STATEMENT','seq[${N}-1]','','');
        case ${N}:
                try {
                        res = ((series_funcp_${N})(registered_functions()[serial].series_f))(${SEQ1},r,order,options);
@@ -127,49 +116,49 @@ $series_switch_statement=generate(
 END_OF_SERIES_SWITCH_STATEMENT
 
 $eval_func_implementation=generate(
-       <<'END_OF_EVAL_FUNC_IMPLEMENTATION','','');
+       <<'END_OF_EVAL_FUNC_IMPLEMENTATION','','','');
 function_options & function_options::eval_func(eval_funcp_${N} e)
 {
        test_and_set_nparams(${N});
-       eval_f=eval_funcp(e);
+       eval_f = eval_funcp(e);
        return *this;
-}        
+}
 END_OF_EVAL_FUNC_IMPLEMENTATION
 
 $evalf_func_implementation=generate(
-       <<'END_OF_EVALF_FUNC_IMPLEMENTATION','','');
+       <<'END_OF_EVALF_FUNC_IMPLEMENTATION','','','');
 function_options & function_options::evalf_func(evalf_funcp_${N} ef)
 {
        test_and_set_nparams(${N});
-       evalf_f=evalf_funcp(ef);
+       evalf_f = evalf_funcp(ef);
        return *this;
-}        
+}
 END_OF_EVALF_FUNC_IMPLEMENTATION
 
 $derivative_func_implementation=generate(
-       <<'END_OF_DERIVATIVE_FUNC_IMPLEMENTATION','','');
+       <<'END_OF_DERIVATIVE_FUNC_IMPLEMENTATION','','','');
 function_options & function_options::derivative_func(derivative_funcp_${N} d)
 {
        test_and_set_nparams(${N});
-       derivative_f=derivative_funcp(d);
+       derivative_f = derivative_funcp(d);
        return *this;
-}        
+}
 END_OF_DERIVATIVE_FUNC_IMPLEMENTATION
 
 $series_func_implementation=generate(
-       <<'END_OF_SERIES_FUNC_IMPLEMENTATION','','');
+       <<'END_OF_SERIES_FUNC_IMPLEMENTATION','','','');
 function_options & function_options::series_func(series_funcp_${N} s)
 {
        test_and_set_nparams(${N});
-       series_f=series_funcp(s);
+       series_f = series_funcp(s);
        return *this;
-}        
+}
 END_OF_SERIES_FUNC_IMPLEMENTATION
 
 $interface=<<END_OF_INTERFACE;
 /** \@file function.h
  *
- *  Interface to abstract class function (new function concept). */
+ *  Interface to class of symbolic functions. */
 
 /*
  *  This file was generated automatically by function.pl.
@@ -199,7 +188,7 @@ $interface=<<END_OF_INTERFACE;
 #include <string>
 #include <vector>
 
-// CINT needs <algorithm> to work properly with <vector> 
+// CINT needs <algorithm> to work properly with <vector>
 #include <algorithm>
 
 #include "exprseq.h"
@@ -212,19 +201,14 @@ $declare_function_macro
 const unsigned function_index_##NAME= \\
        GiNaC::function::register_new(GiNaC::function_options(#NAME).OPT);
 
-#define REGISTER_FUNCTION_OLD(NAME,E,EF,D,S) \\
-const unsigned function_index_##NAME= \\
-       GiNaC::function::register_new(GiNaC::function_options(#NAME). \\
-                                     eval_func(E). \\
-                                     evalf_func(EF). \\
-                                     derivative_func(D). \\
-                                     series_func(S));
+// The TYPECHECK-macros were used inside the _evalf() functions.  They are
+// considered obsolete now:  (FIXME: remove them)
 
 #define BEGIN_TYPECHECK \\
 bool automatic_typecheck=true;
 
 #define TYPECHECK(VAR,TYPE) \\
-if (!is_ex_exactly_of_type(VAR,TYPE)) { \\
+if (!is_exactly_a<TYPE>(VAR)) { \\
        automatic_typecheck=false; \\
 } else
 
@@ -242,6 +226,7 @@ if (!automatic_typecheck) { \\
 namespace GiNaC {
 
 class function;
+class symmetry;
 
 typedef ex (* eval_funcp)();
 typedef ex (* evalf_funcp)();
@@ -255,9 +240,17 @@ $typedef_derivative_funcp
 $typedef_series_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 (* derivative_funcp_exvector)(const exvector &, unsigned);
+typedef ex (* series_funcp_exvector)(const exvector &, const relational &, int, unsigned);
+
 class function_options
 {
        friend class function;
+       friend class fderivative;
 public:
        function_options();
        function_options(std::string const & n, std::string const & tn=std::string());
@@ -271,14 +264,21 @@ $evalf_func_interface
 $derivative_func_interface
 $series_func_interface
 // end of generated lines
+       function_options & eval_func(eval_funcp_exvector e);
+       function_options & evalf_func(evalf_funcp_exvector ef);
+       function_options & derivative_func(derivative_funcp_exvector d);
+       function_options & series_func(series_funcp_exvector s);
+
        function_options & set_return_type(unsigned rt, unsigned rtt=0);
        function_options & do_not_evalf_params(void);
        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);
        void test_and_set_nparams(unsigned n);
        std::string get_name(void) const { return name; }
        unsigned get_nparams(void) const { return nparams; }
+       bool has_derivative(void) const { return derivative_f != NULL; }
 
 protected:
        std::string name;
@@ -302,7 +302,14 @@ protected:
        unsigned remember_assoc_size;
        unsigned remember_strategy;
 
+       bool eval_use_exvector_args;
+       bool evalf_use_exvector_args;
+       bool derivative_use_exvector_args;
+       bool series_use_exvector_args;
+
        unsigned functions_with_same_name;
+
+       ex symtree;
 };
 
 /** The class function is used to implement builtin functions like sin, cos...
@@ -329,10 +336,10 @@ public:
 $constructors_interface
        // end of generated lines
        function(unsigned ser, const exprseq & es);
-       function(unsigned ser, const exvector & v, bool discardable=0);
+       function(unsigned ser, const exvector & v, bool discardable = false);
        function(unsigned ser, exvector * vp); // vp will be deleted
 
-       // functions overriding virtual functions from bases classes
+       // functions overriding virtual functions from base classes
 public:
        void print(const print_context & c, unsigned level = 0) const;
        unsigned precedence(void) const {return 70;}
@@ -344,12 +351,12 @@ public:
        ex evalf(int level=0) const;
        unsigned calchash(void) const;
        ex series(const relational & r, int order, unsigned options = 0) const;
-       bool match(const ex & pattern, lst & repl_lst) const;
        ex thisexprseq(const exvector & v) const;
        ex thisexprseq(exvector * vp) const;
 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(void) const;
        unsigned return_type_tinfo(void) const;
        
@@ -364,10 +371,11 @@ protected:
        void store_remember_table(ex const & result) const;
 public:
        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(void) const {return serial;}
        std::string get_name(void) const;
-       
+
 // member variables
 
 protected:
@@ -375,13 +383,15 @@ protected:
 };
 
 // utility functions/macros
-inline const function &ex_to_function(const ex &e)
+
+/** Specialization of is_exactly_a<function>(obj) for objects of type function. */
+template<> inline bool is_exactly_a<function>(const basic & obj)
 {
-       return static_cast<const function &>(*e.bp);
+       return obj.tinfo()==TINFO_function;
 }
 
 #define is_ex_the_function(OBJ, FUNCNAME) \\
-       (is_ex_exactly_of_type(OBJ, function) && static_cast<GiNaC::function *>(OBJ.bp)->get_serial() == function_index_##FUNCNAME)
+       (is_exactly_a<GiNaC::function>(OBJ) && ex_to<GiNaC::function>(OBJ).get_serial() == function_index_##FUNCNAME)
 
 } // namespace GiNaC
 
@@ -392,7 +402,7 @@ END_OF_INTERFACE
 $implementation=<<END_OF_IMPLEMENTATION;
 /** \@file function.cpp
  *
- *  Implementation of class function. */
+ *  Implementation of class of symbolic functions. */
 
 /*
  *  This file was generated automatically by function.pl.
@@ -421,11 +431,14 @@ $implementation=<<END_OF_IMPLEMENTATION;
 #include <list>
 
 #include "function.h"
+#include "fderivative.h"
 #include "ex.h"
 #include "lst.h"
+#include "symmetry.h"
 #include "print.h"
 #include "archive.h"
 #include "inifcns.h"
+#include "tostring.h"
 #include "utils.h"
 #include "debugmsg.h"
 #include "remember.h"
@@ -455,29 +468,33 @@ function_options::~function_options()
 void function_options::initialize(void)
 {
        set_name("unnamed_function","\\\\mbox{unnamed}");
-       nparams=0;
-       eval_f=evalf_f=derivative_f=series_f=0;
-       evalf_params_first=true;
-       use_return_type=false;
-       use_remember=false;
-       functions_with_same_name=1;
+       nparams = 0;
+       eval_f = evalf_f = derivative_f = series_f = 0;
+       evalf_params_first = true;
+       use_return_type = false;
+       eval_use_exvector_args = false;
+       evalf_use_exvector_args = false;
+       derivative_use_exvector_args = false;
+       series_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;
-       }
+       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;
+       TeX_name = tn;
        return *this;
 }
 
@@ -488,17 +505,43 @@ $derivative_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::derivative_func(derivative_funcp_exvector d)
+{
+       derivative_use_exvector_args = true;
+       derivative_f = derivative_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, unsigned rtt)
 {
-       use_return_type=true;
-       return_type=rt;
-       return_type_tinfo=rtt;
+       use_return_type = true;
+       return_type = rt;
+       return_type_tinfo = rtt;
        return *this;
 }
 
 function_options & function_options::do_not_evalf_params(void)
 {
-       evalf_params_first=false;
+       evalf_params_first = false;
        return *this;
 }
 
@@ -506,23 +549,29 @@ 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;
+       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;
+       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;
+               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
@@ -533,6 +582,10 @@ void function_options::test_and_set_nparams(unsigned n)
        }
 }
 
+/** This can be used as a hook for external applications. */
+unsigned function::current_serial = 0;
+
+
 GINAC_IMPLEMENT_REGISTERED_CLASS(function, exprseq)
 
 //////////
@@ -551,13 +604,14 @@ function::function() : serial(0)
 
 void function::copy(const function & other)
 {
-       exprseq::copy(other);
-       serial=other.serial;
+       inherited::copy(other);
+       serial = other.serial;
 }
 
 void function::destroy(bool call_parent)
 {
-       if (call_parent) exprseq::destroy(call_parent);
+       if (call_parent)
+               inherited::destroy(call_parent);
 }
 
 //////////
@@ -615,7 +669,7 @@ function::function(const archive_node &n, const lst &sym_lst) : inherited(n, sym
                                serial = ser;
                                return;
                        }
-                       i++; ser++;
+                       ++i; ++ser;
                }
                throw (std::runtime_error("unknown function '" + s + "' in archive"));
        } else
@@ -637,7 +691,7 @@ void function::archive(archive_node &n) const
 }
 
 //////////
-// functions overriding virtual functions from bases classes
+// functions overriding virtual functions from base classes
 //////////
 
 // public
@@ -656,7 +710,7 @@ void function::print(const print_context & c, unsigned level) const
                    << ", nops=" << nops()
                    << std::endl;
                unsigned delta_indent = static_cast<const print_tree &>(c).delta_indent;
-               for (unsigned i=0; i<nops(); ++i)
+               for (unsigned i=0; i<seq.size(); ++i)
                        seq[i].print(c, level + delta_indent);
                c.s << std::string(level + delta_indent, ' ') << "=====" << std::endl;
 
@@ -664,7 +718,8 @@ void function::print(const print_context & c, unsigned level) const
 
                // Print function name in lowercase
                std::string lname = registered_functions()[serial].name;
-               for (unsigned i=0; i<lname.size(); i++)
+               unsigned num = lname.size();
+               for (unsigned i=0; i<num; i++)
                        lname[i] = tolower(lname[i]);
                c.s << lname << "(";
 
@@ -672,13 +727,13 @@ void function::print(const print_context & c, unsigned level) const
                exvector::const_iterator it = seq.begin(), itend = seq.end();
                while (it != itend) {
                        it->print(c);
-                       it++;
+                       ++it;
                        if (it != itend)
                                c.s << ",";
                }
                c.s << ")";
 
-       } else if is_of_type(c, print_latex) {
+       } else if (is_of_type(c, print_latex)) {
                c.s << registered_functions()[serial].TeX_name;
                printseq(c, '(', ',', ')', exprseq::precedence(), function::precedence());
        } else {
@@ -689,22 +744,26 @@ void function::print(const print_context & c, unsigned level) const
 
 ex function::expand(unsigned options) const
 {
-       return this->setflag(status_flags::expanded);
+       // 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;
 }
 
 int function::degree(const ex & s) const
 {
-       return is_equal(*s.bp) ? 1 : 0;
+       return is_equal(ex_to<basic>(s)) ? 1 : 0;
 }
 
 int function::ldegree(const ex & s) const
 {
-       return is_equal(*s.bp) ? 1 : 0;
+       return is_equal(ex_to<basic>(s)) ? 1 : 0;
 }
 
 ex function::coeff(const ex & s, int n) const
 {
-       if (is_equal(*s.bp))
+       if (is_equal(ex_to<basic>(s)))
                return n==1 ? _ex1() : _ex0();
        else
                return n==0 ? ex(*this) : _ex0();
@@ -719,17 +778,35 @@ ex function::eval(int level) const
                return function(serial,evalchildren(level));
        }
 
-       if (registered_functions()[serial].eval_f==0) {
+       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 != INT_MAX) {
+                       // Something has changed while sorting arguments, more evaluations later
+                       if (sig == 0)
+                               return _ex0();
+                       return ex(sig) * thisexprseq(v);
+               }
+       }
+
+       if (opt.eval_f==0) {
                return this->hold();
        }
 
-       bool use_remember=registered_functions()[serial].use_remember;
+       bool use_remember = opt.use_remember;
        ex eval_result;
        if (use_remember && lookup_remember_table(eval_result)) {
                return eval_result;
        }
-
-       switch (registered_functions()[serial].nparams) {
+       current_serial = serial;
+       if (registered_functions()[serial].eval_use_exvector_args)
+               eval_result = ((eval_funcp_exvector)(registered_functions()[serial].eval_f))(seq);
+       else
+       switch (opt.nparams) {
                // the following lines have been generated for max. ${maxargs} parameters
 ${eval_switch_statement}
                // end of generated lines
@@ -746,11 +823,27 @@ ex function::evalf(int level) const
 {
        GINAC_ASSERT(serial<registered_functions().size());
 
-       exvector eseq=evalfchildren(level);
+       // Evaluate children first
+       exvector eseq;
+       if (level == 1)
+               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 (registered_functions()[serial].evalf_f==0) {
                return function(serial,eseq).hold();
        }
+       current_serial = serial;
+       if (registered_functions()[serial].evalf_use_exvector_args)
+               return ((evalf_funcp_exvector)(registered_functions()[serial].evalf_f))(seq);
        switch (registered_functions()[serial].nparams) {
                // the following lines have been generated for max. ${maxargs} parameters
 ${evalf_switch_statement}
@@ -794,6 +887,15 @@ ex function::series(const relational & r, int order, unsigned options) const
                return basic::series(r, order);
        }
        ex res;
+       current_serial = serial;
+       if (registered_functions()[serial].series_use_exvector_args) {
+               try {
+                       res = ((series_funcp_exvector)(registered_functions()[serial].series_f))(seq, r, order, options);
+               } catch (do_taylor) {
+                       res = basic::series(r, order, options);
+               }
+               return res;
+       }
        switch (registered_functions()[serial].nparams) {
                // the following lines have been generated for max. ${maxargs} parameters
 ${series_switch_statement}
@@ -802,46 +904,23 @@ ${series_switch_statement}
        throw(std::logic_error("function::series(): invalid nparams"));
 }
 
-bool function::match(const ex & pattern, lst & repl_lst) const
-{
-       // Serial number must match
-       if (is_ex_of_type(pattern, function) && serial != ex_to_function(pattern).serial)
-               return false;
-       return inherited::match(pattern, repl_lst);
-}
-
 // 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 == function_index_Order) {
                // Order Term function only differentiates the argument
                return Order(seq[0].diff(s));
-       } else if (serial == function_index_Derivative) {
-               // Inert derivative performs chain rule on the first argument only, and
-               // adds differentiation parameter to list (second argument)
-               GINAC_ASSERT(is_ex_exactly_of_type(seq[0], function));
-               GINAC_ASSERT(is_ex_exactly_of_type(seq[1], function));
-               ex fcn = seq[0];
-               ex arg_diff;
-               for (unsigned i=0; i!=fcn.nops(); i++) {
-                       arg_diff = fcn.op(i).diff(s);
-                       if (!arg_diff.is_zero()) {
-                               lst new_lst = ex_to_lst(seq[1]);
-                               new_lst.append(i);
-                               result += arg_diff * Derivative(fcn, new_lst);
-                       }
-               }
        } else {
                // Chain rule
                ex arg_diff;
-               for (unsigned i=0; i!=seq.size(); i++) {
+               unsigned num = seq.size();
+               for (unsigned 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
@@ -858,37 +937,47 @@ ex function::derivative(const symbol & s) const
 int function::compare_same_type(const basic & other) const
 {
        GINAC_ASSERT(is_of_type(other, function));
-       const function & o=static_cast<function &>(const_cast<basic &>(other));
+       const function & o = static_cast<const function &>(other);
 
-       if (serial!=o.serial) {
+       if (serial != o.serial)
                return serial < o.serial ? -1 : 1;
-       }
-       return exprseq::compare_same_type(o);
+       else
+               return exprseq::compare_same_type(o);
 }
 
 bool function::is_equal_same_type(const basic & other) const
 {
        GINAC_ASSERT(is_of_type(other, function));
-       const function & o=static_cast<function &>(const_cast<basic &>(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_of_type(other, function));
+       const function & o = static_cast<const function &>(other);
 
-       if (serial!=o.serial) return false;
-       return exprseq::is_equal_same_type(o);
+       return serial == o.serial;
 }
 
 unsigned function::return_type(void) const
 {
-       if (seq.size()==0) {
+       if (seq.empty())
                return return_types::commutative;
-       }
-       return (*seq.begin()).return_type();
+       else
+               return seq.begin()->return_type();
 }
-   
+
 unsigned function::return_type_tinfo(void) const
 {
-       if (seq.size()==0) {
+       if (seq.empty())
                return tinfo_key;
-       }
-       return (*seq.begin()).return_type_tinfo();
+       else
+               return seq.begin()->return_type_tinfo();
 }
 
 //////////
@@ -907,14 +996,18 @@ ex function::pderivative(unsigned diff_param) const // partial differentiation
 {
        GINAC_ASSERT(serial<registered_functions().size());
        
-       if (registered_functions()[serial].derivative_f==0) {
-               return Derivative(*this, lst(ex(diff_param)));
-       }
+       // No derivative defined? Then return abstract derivative object
+       if (registered_functions()[serial].derivative_f == NULL)
+               return fderivative(serial, diff_param, seq);
+
+       current_serial = serial;
+       if (registered_functions()[serial].derivative_use_exvector_args)
+               return ((derivative_funcp_exvector)(registered_functions()[serial].derivative_f))(seq, diff_param);
        switch (registered_functions()[serial].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"));
 }
 
@@ -938,10 +1031,10 @@ void function::store_remember_table(ex const & result) const
 
 unsigned function::register_new(function_options const & opt)
 {
-       unsigned same_name=0;
+       unsigned same_name = 0;
        for (unsigned i=0; i<registered_functions().size(); ++i) {
                if (registered_functions()[i].name==opt.name) {
-                       same_name++;
+                       ++same_name;
                }
        }
        if (same_name>=opt.functions_with_same_name) {
@@ -949,14 +1042,14 @@ unsigned function::register_new(function_options const & opt)
                // usually executed before main(), so the exception could not
                // caught anyhow
                std::cerr << "WARNING: function name " << opt.name
-                                 << " already in use!" << std::endl;
+                         << " 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));
+                                                opt.remember_assoc_size,
+                                                opt.remember_strategy));
        } else {
                remember_table::remember_tables().push_back(remember_table());
        }
@@ -972,8 +1065,8 @@ unsigned function::find_function(const std::string &name, unsigned nparams)
        while (i != end) {
                if (i->get_name() == name && i->get_nparams() == nparams)
                        return serial;
-               i++;
-               serial++;
+               ++i;
+               ++serial;
        }
        throw (std::runtime_error("no function '" + name + "' with " + ToString(nparams) + " parameters defined"));
 }