libgiac-dev 1.2.3.57+dfsg1-2build3 / usr / include / giac / gen.h

// -*- mode:C++ ; compile-command: "g++ -I.. -g -c -DHAVE_CONFIG_H -DIN_GIAC gen.cc" -*-
/*
 *  Copyright (C) 2001,2014 B. Parisse, Institut Fourier, 38402 St Martin d'Heres
 *
 *  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 3 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, see <http://www.gnu.org/licenses/>.
 */
#ifndef _GIAC_GEN_H
#define _GIAC_GEN_H

/* Warning: the size of a gen depend on the architecture and of compile-time flags
   Define -DSMARTPTR64 on 64 bit CPU if the pointers allocated by new are 48 bits
   this will make sizeof(gen)==8 instead of 16
   Currently the address of pointers is obtained by using the reserved and val fields
   (48 bits) and adding 00 for the most significant bits
   On systems that use pointers above 0x00ffffffff it might be better to use a table 
   of most significants 32 bits addresses (refered by the reserved field) 
   and use the val field for offset.
   Define -DDOUBLEVAL if you did not define SMARTPTR64 and want full double precision
   (53 bit mantissa). Otherwise, the 8 less significant bits will be used for the type
   field of a gen, i.e. 0x01 for a double, hence 45 bit mantissa will be used for doubles
   Using full double precision increases sizeof(gen) to 12 on a 32 bits CPU 
   (and 16 on a 64 bits CPU)
 */

// FIXME: macros defined in config.h are not welcome in a public header!
#ifdef HAVE_CONFIG_H
#include "config.h"
#endif
#include "first.h"

// #include <gmp.h>
#ifdef USE_GMP_REPLACEMENTS
#undef HAVE_GMPXX_H
#undef HAVE_LIBMPFR
#endif
#ifdef HAVE_GMPXX_H
#include <gmpxx.h>
#endif
#ifdef HAVE_LIBMPFR
#include <mpfr.h>
// #include <mpf2mpfr.h>
#endif
#ifdef HAVE_LIBMPFI
#include <mpfi.h>
#endif
#include <iostream>
#include <string>
#include "vector.h"
#include <map>
#include "dispatch.h"
#include "vecteur.h"
#include "fraction.h"
#include "poly.h"
#include "giacintl.h"
#include <complex>
#include <stdlib.h>
#ifdef STATIC_BUILTIN_LEXER_FUNCTIONS
#include "static.h"
#endif

#ifndef NO_NAMESPACE_GIAC
namespace giac {
#endif // ndef NO_NAMESPACE_GIAC


#ifdef USE_GMP_REPLACEMENTS
#undef HAVE_GMPXX_H
#undef HAVE_LIBMPFR
#endif

  void my_mpz_gcd(mpz_t &z,const mpz_t & A,const mpz_t & B);

  class gen ; 
  // errors
  void settypeerr(GIAC_CONTEXT0);
  void setsizeerr(GIAC_CONTEXT0);
  void setdimerr(GIAC_CONTEXT0);
  void settypeerr(const std::string & s);
  void setsizeerr(const std::string & s);
  void setdimerr(const std::string & s);
  void divisionby0err(const gen &,GIAC_CONTEXT0);
  void cksignerr(const gen &,GIAC_CONTEXT0);
  void invalidserieserr(const std::string &,GIAC_CONTEXT0);
  void toofewargs(const std::string & s,GIAC_CONTEXT0);
  void toomanyargs(const std::string & s,GIAC_CONTEXT0);
  void maxordererr(GIAC_CONTEXT0);
  void setstabilityerr(GIAC_CONTEXT0);

  gen undeferr(const std::string & s);
  gen gentypeerr(GIAC_CONTEXT0);
  void gentypeerr(gen & g,GIAC_CONTEXT);
  gen gensizeerr(GIAC_CONTEXT0);
  void gensizeerr(gen & g,GIAC_CONTEXT);
  gen gendimerr(GIAC_CONTEXT0);
  void gendimerr(gen & g,GIAC_CONTEXT);
  gen gentypeerr(const std::string & s);
  void gentypeerr(const char * ch,gen & g);
  gen gensizeerr(const std::string & s);
  void gensizeerr(const char * ch,gen & g);
  gen gendimerr(const std::string & s);
  void gensizeerr(const char * ch,gen & g);
  gen gendivisionby0err(const gen &,GIAC_CONTEXT0);
  gen gencksignerr(const gen &,GIAC_CONTEXT0);
  gen geninvalidserieserr(const std::string &,GIAC_CONTEXT0);
  gen gentoofewargs(const std::string & s,GIAC_CONTEXT0);
  gen gentoomanyargs(const std::string & s,GIAC_CONTEXT0);
  gen genmaxordererr(GIAC_CONTEXT0);
  gen genstabilityerr(GIAC_CONTEXT0);

  // short integer arithmetic
  int absint(int a);
  int giacmin(int a,int b);
  int giacmax(int a,int b);
  int invmod(int n,int modulo);
  unsigned invmod(unsigned a,int b);
  int invmod(longlong a,int b);
#ifdef INT128
  int invmod(int128_t a,int b);
  inline int smod(int128_t r,int m){
    int R=r%m;
    return smod(R,m);
  }
#endif
  int gcd(int a,int b);
  inline int smod_adjust(int r,int m){ // precondition -m<r<m
    r += (unsigned(r)>>31)*m; // make positive
    return r-(unsigned((m>>1)-r)>>31)*m;
  }
  int smod(int a,int b); // where b is assumed to be positive
  int smod(longlong a,int b); 
  int simplify(int & a,int & b);

  struct ref_mpz_t {
    volatile ref_count_t ref_count;
    mpz_t z;
    ref_mpz_t():ref_count(1) {mpz_init(z);}
    ref_mpz_t(size_t nbits):ref_count(1) {mpz_init2(z,int(nbits));}
    ref_mpz_t(const mpz_t & Z): ref_count(1) { mpz_init_set(z,Z); }
    ~ref_mpz_t() { mpz_clear(z); }
  };
  class identificateur;
  struct ref_identificateur; // in identificateur.h
  struct symbolic;
  struct ref_symbolic; // in symbolic.h
  class unary_function_eval;
  struct unary_function_ptr;
  typedef const unary_function_ptr *  const_unary_function_ptr_ptr;
  typedef const unary_function_eval *  const_unary_function_eval_ptr;
  struct ref_unary_function_ptr; // in unary.h 
  struct eqwdata;
  struct ref_eqwdata ; // defined below after gen
  struct ref_complex;
  struct ref_algext;
  struct ref_modulo;
  // Graphic object
  struct grob {
    void (* grob_draw)(void);
    int (* grob_handle) (int);
    void * grob_data;
  };
  struct ref_grob {
    volatile ref_count_t ref_count;
    grob g;
    ref_grob(const grob & G):ref_count(1),g(G) {}
  };
  class gen_user;
  struct ref_gen_user ; // user defined type
  struct ref_string {
    volatile ref_count_t ref_count;
    std::string s;
    ref_string(const std::string & S):ref_count(1),s(S) {}
  };
  template <class T> class tensor;

  typedef tensor<gen> polynome;
  typedef std::vector< facteur< polynome > > factorization;

  template<class T> class Tref_tensor; // in poly.h
  typedef Tref_tensor<gen> ref_polynome;
  typedef Tfraction<gen> fraction;
  template<class T> class Tref_fraction; 
  typedef Tref_fraction<gen> ref_fraction;

  struct ref_vecteur;
  void delete_ref_vecteur(ref_vecteur * ptr);
  ref_vecteur * new_ref_vecteur(const vecteur & v);
  ref_symbolic * new_ref_symbolic(const symbolic & s);

  template<class T> class Tref_fraction; // in fraction.h
  struct ref_void_pointer {
    volatile ref_count_t ref_count;
    void * p;
    ref_void_pointer(void * P):ref_count(1),p(P) {}
  };


  struct monome;
  // sparse polynomials: uncomment one of the 2 next lines
#ifdef DEBUG_SUPPORT
  typedef dbgprint_vector<monome> sparse_poly1; // debugging support
#else
  typedef std::vector<monome> sparse_poly1; // no debug. support
#endif
  struct ref_sparse_poly1;

  // arbitrary precision floats hierarchy (value or interval)
  std::string printmpf_t(const mpf_t & inf);
  class real_object {
  public:
#ifdef HAVE_LIBMPFR
    mpfr_t inf;
#else
    mpf_t inf;
#endif
    real_object(double d); 
#ifdef HAVE_LIBMPFR
    real_object(const mpfr_t & d); 
    real_object(const mpf_t & d); 
#else
    real_object(const mpf_t & d); 
#endif
    real_object(const gen & g);
    real_object(const gen & g,unsigned int precision);
    real_object() ;
    virtual std::string print(GIAC_CONTEXT) const;
    const char * dbgprint() const { 
      static std::string s; 
      s=this->print(0);
#if 0 // ndef NSPIRE
      CERR << s << std::endl;
#endif
      return s.c_str(); 
    }
    virtual ~real_object() { 
#ifdef HAVE_LIBMPFR
      mpfr_clear(inf);
#else
      mpf_clear(inf); 
#endif
    }
    virtual real_object & operator = (const real_object & g);
    real_object (const real_object & g) ;
    virtual gen addition (const gen & g,GIAC_CONTEXT) const;
    gen operator + (const gen & g) const;
    virtual gen operator + (const real_object & g) const;
    virtual gen multiply (const gen & g,GIAC_CONTEXT) const;
    gen operator * (const gen & g) const;
    virtual gen operator * (const real_object & g) const;
    virtual gen divide (const gen & g,GIAC_CONTEXT) const;
    gen operator / (const gen & g) const;
    virtual gen substract (const gen & g,GIAC_CONTEXT) const;
    virtual gen operator / (const real_object & g) const;
    gen operator - (const gen & g) const;
    virtual gen operator - (const real_object & g) const;
    virtual gen operator -() const;
    virtual gen inv() const;
    virtual gen sqrt() const;
    virtual gen abs() const;
    virtual gen exp() const;
    virtual gen log() const;
    virtual gen sin() const;
    virtual gen cos() const;
    virtual gen tan() const;
    virtual gen sinh() const;
    virtual gen cosh() const;
    virtual gen tanh() const;
    virtual gen asin() const;
    virtual gen acos() const;
    virtual gen atan() const;
    virtual gen asinh() const;
    virtual gen acosh() const;
    virtual gen atanh() const;
    virtual bool is_zero() const;
    virtual bool maybe_zero() const;
    virtual bool is_inf() const;
    virtual bool is_nan() const;
    virtual int is_positive() const;
    virtual double evalf_double() const;
  };
  struct ref_real_object {
    volatile ref_count_t ref_count;
    real_object r;
    ref_real_object():ref_count(1) {}
    ref_real_object(const real_object & R):ref_count(1),r(R) {}
  };
  gen real2int(const gen & g,GIAC_CONTEXT);
  gen real2double(const gen & g);
  class real_interval : public real_object {
  public:
#ifdef HAVE_LIBMPFI
    mpfi_t infsup;
#else
#ifdef HAVE_LIBMPFR
    mpfr_t sup;
#else
    mpf_t sup;
#endif
#endif
    real_interval(){
#ifdef HAVE_LIBMPFI
      mpfi_init_set_fr(infsup,inf);
#else
#ifdef HAVE_LIBMPFR
      mpfr_init_set(sup,inf,GMP_RNDN); 
#else
      mpf_init_set(sup,inf); 
#endif
#endif
    }
#ifdef HAVE_LIBMPFI
    real_interval(const mpfi_t & interv); 
#endif
    real_interval(const real_object & r):real_object(r) { 
#ifdef HAVE_LIBMPFI
      mpfi_init2(infsup,mpfr_get_prec(r.inf));
      mpfi_set_fr(infsup,r.inf);
#else
#ifdef HAVE_LIBMPFR
      mpfr_init_set(sup,r.inf,GMP_RNDN); 
#else
      mpf_init_set(sup,r.inf); 
#endif
#endif
    }
    real_interval(const real_interval & r):real_object(r) { 
#ifdef HAVE_LIBMPFI
      mpfi_init2(infsup,mpfi_get_prec(r.infsup));
      mpfi_set(infsup,r.infsup);
#else
#ifdef HAVE_LIBMPFR
      mpfr_init_set(sup,r.sup,GMP_RNDN); 
#else
      mpf_init_set(sup,r.sup); 
#endif
#endif
    }
    virtual ~real_interval() { 
#ifdef HAVE_LIBMPFI
      mpfi_clear(infsup); 
#else
#ifdef HAVE_LIBMPFR
      mpfr_clear(sup); 
#else
      mpf_clear(sup); 
#endif
#endif
    }
    virtual real_object & operator = (const real_interval & g) ;
    virtual real_object & operator = (const real_object & g) ;
    virtual gen addition (const gen & g,GIAC_CONTEXT) const;
    virtual gen operator + (const real_object & g) const;
    virtual real_interval operator + (const real_interval & g) const;
    virtual gen multiply (const gen & g,GIAC_CONTEXT) const;
    virtual gen operator * (const real_object & g) const;
    virtual real_interval operator * (const real_interval & g) const;
    virtual gen divide (const gen & g,GIAC_CONTEXT) const;
    virtual gen substract (const gen & g,GIAC_CONTEXT) const;
    virtual gen operator - (const real_object & g) const;
    virtual real_interval operator - (const real_interval & g) const ;
    virtual gen operator -() const;
    virtual bool is_zero () const ;
    virtual bool maybe_zero () const ;
    virtual int is_positive() const ;
    virtual bool is_inf() const;
    virtual bool is_nan() const;
    virtual gen inv() const;
    virtual gen sqrt() const;
    virtual gen abs() const;
    virtual gen exp() const;
    virtual gen log() const;
    virtual gen sin() const;
    virtual gen cos() const;
    virtual gen tan() const;
    virtual gen sinh() const;
    virtual gen cosh() const;
    virtual gen tanh() const;
    virtual gen asin() const;
    virtual gen acos() const;
    virtual gen atan() const;
    virtual gen asinh() const;
    virtual gen acosh() const;
    virtual gen atanh() const;
  };
  struct ref_real_interval {
    volatile ref_count_t ref_count;
    real_interval r; // assumes that storage of real_object inside real_interval is first
    ref_real_interval():ref_count(1) {}
    ref_real_interval(const real_interval & R):ref_count(1),r(R) {}
  };
  std::string print_binary(const real_object & r);
  gen read_binary(const std::string & s,unsigned int precision);
  // Convert g to a real or complex object of precision nbits
  gen accurate_evalf(const gen & g,int nbits);
  vecteur accurate_evalf(const vecteur & v,int nbits);
  std::string print_DOUBLE_(double d,GIAC_CONTEXT);

#if 1 // def NSPIRE
  class comparegen {
  public:
    bool operator () (const gen & a,const gen & b) const;
  };
  typedef std::map<gen,gen,comparegen> gen_map;
#else
  typedef std::map<gen,gen,const std::pointer_to_binary_function < const gen &, const gen &, bool> > gen_map;
#endif
  struct ref_gen_map;

  class my_mpz;

#ifdef NO_UNARY_FUNCTION_COMPOSE
  class unary_function_eval;
#else
  class unary_function_abstract;
#endif

  struct alias_unary_function_eval;
  struct unary_function_ptr {
#ifdef NO_UNARY_FUNCTION_COMPOSE
    // const unary_function_eval * _ptr;
    size_t _ptr;
    // int quoted; // will be used to avoid evaluation of args by eval
    // constructors
    // lexer_register is true to add dynamically the function name
    // to the list of functions names recognized by the lexer
    unary_function_ptr():_ptr(0) {} ;
    unary_function_ptr(const unary_function_eval * myptr):_ptr((size_t)myptr) {} ;
    // unary_function_ptr(const unary_function_eval * myptr,int parser_token);
    unary_function_ptr(const unary_function_eval * myptr,int myquoted,int parser_token);
    // unary_function_ptr(const alias_unary_function_eval * myptr,int parser_token);
    unary_function_ptr(const alias_unary_function_eval * myptr,int myquoted,int parser_token);
#else // NO_UNARY_FUNCTION_COMPOSE
    const unary_function_abstract * _ptr;
    // long * ref_count;
    // int quoted; // will be used to avoid evaluation of args by eval
    // constructors
    // lexer_register is true to add dynamically the function name
    // to the list of functions names recognized by the lexer
    // unary_function_ptr(const unary_function_abstract & myptr);
    unary_function_ptr():_ptr(0) {} ;
    unary_function_ptr(const unary_function_abstract * myptr):_ptr(myptr) {} ;
    // unary_function_ptr(const unary_function_abstract * myptr,int parser_token) ;
    // unary_function_ptr(const unary_function_abstract & myptr,int myquoted,int parser_token=0);
    unary_function_ptr(const unary_function_abstract * myptr,int myquoted,int parser_token);
    // unary_function_ptr(const unary_function_ptr & myptr);
    // unary_function_ptr(const alias_unary_function_eval * myptr,int parser_token);
    unary_function_ptr(const alias_unary_function_eval * myptr,int myquoted,int parser_token);
#endif // NO_UNARY_FUNCTION_COMPOSE
    // ~unary_function_ptr();
    // unary_function_ptr & operator = (const unary_function_ptr & acopier);
    gen operator () (const gen & arg,GIAC_CONTEXT) const;
#ifdef NO_UNARY_FUNCTION_COMPOSE
    inline unary_function_eval * ptr() const {
      return (unary_function_eval *) (((size_t) _ptr) & ~(uintptr_t)3);
#ifdef x86_64
      return (unary_function_eval *) (((ulonglong ) _ptr) & 0xfffffffffffffffc);
#else
      return (unary_function_eval *) (((size_t) _ptr) & 0xfffffffc);
#endif
    }
#else // NO_UNARY_FUNCTION_COMPOSE
    inline unary_function_abstract * ptr () const
    {
      return (unary_function_abstract *) (((ulonglong ) _ptr) & ~(uintptr_t)3);
#ifdef x86_64
      return (unary_function_abstract *) (((ulonglong ) _ptr) & 0xfffffffffffffffc);
#else
      return (unary_function_abstract *) (((size_t) _ptr) & 0xfffffffc);
#endif
    }
#endif // NO_UNARY_FUNCTION_COMPOSE
    bool quoted() const ;
    inline bool operator ==(const unary_function_ptr & u) const { 
      // if (&u==this) return true; 
      return ((ulonglong)(_ptr) & ~(uintptr_t)3 )  == ((ulonglong)( u._ptr) & ~(uintptr_t)3 );
#ifdef x86_64
      return ((ulonglong)(_ptr) & 0xfffffffffffffffc)  == ((ulonglong)( u._ptr) & 0xfffffffffffffffc ); 
#else
      return ((size_t)(_ptr) & 0xfffffffc) == ((size_t)(u._ptr) & 0xfffffffc); 
#endif
    }
    inline bool operator !=(const unary_function_ptr & u) const { return !(*this==u); }
    inline bool operator ==(const unary_function_ptr * u) const { 
      // if (&u==this) return true; 
      return u && ( ((ulonglong)(_ptr) &  ~(uintptr_t)3 ) == ((ulonglong)(u->_ptr) &  ~(uintptr_t)3) ); 
#ifdef x86_64
      return u && ( ((ulonglong)(_ptr) & 0xfffffffffffffffc) == ((ulonglong)(u->_ptr) & 0xfffffffffffffffc) ); 
#else
      return u && ( ((size_t)(_ptr) & 0xfffffffc) == ((size_t)(u->_ptr) & 0xfffffffc ) ); 
#endif
    }
    inline bool operator !=(const unary_function_ptr * u) const { return !(*this==u); }
    const char * dbgprint() const;
  };

  void delete_ptr(signed char subtype,short int type_save,ref_mpz_t * ptr_save);
  // FIXME: for little-endian check if type/unused/subtype order is correct!
  class gen {
  public:
#ifdef GIAC_TYPE_ON_8BITS
    unsigned char type;  // see dispatch.h
#else
    unsigned char type:5;  // 32 types is enough, keep 3 bits more for double
    unsigned char type_unused:3; 
#endif
    signed char subtype;
    unsigned short reserved; // used if SMARTPTR is defined on 64 bit CPU (16 bits for pointer val)
    union {
      // immediate types
      int val; // immediate int (type _INT_)
#ifdef DOUBLEVAL
      double _DOUBLE_val; // immediate float (type _DOUBLE_)
      giac_float _FLOAT_val;
#endif
#ifndef SMARTPTR64
      // pointer types
      ref_mpz_t * __ZINTptr; // long int (type _ZINT)
      ref_real_object * __REALptr; // extended double (type _REAL)
      ref_complex * __CPLXptr ; // complex as an gen[2] array (type _CPLX)
      ref_identificateur * __IDNTptr; // global name identifier (type _IDNT)
      ref_symbolic * __SYMBptr; // for symbolic objects (type _SYMB)
      ref_modulo * __MODptr;
      ref_algext * __EXTptr; // 2 gens for alg. extension (type ext)
      // alg ext: 1st gen is a std::vector or a fraction, 2nd gen is
      // a/ a std::vector, the minimal monic polynomial (the roots are permutable)
      // b/ a real_complex_rootof given by it's min poly and 
      // c/ another type meaning that the root is expressed in terms
      //    of another rootof, in this case ext_reduce should be called
      // For 2nd order extension, X^2=d is used if d!=1 mod 4
      // X is the positive solution
      // if d=1 mod 4 the equation is X^2-X=(d-1)/4
      Tref_fraction<gen> * __FRACptr; // fraction (type _FRAC)
      Tref_tensor<gen> * __POLYptr ; // multidim. sparse polynomials (type poly)
      // _VECTosite types (std::vector<>)
      ref_vecteur * __VECTptr ; // vecteur: std::vectors & dense_POLY1 (type _VECT)
      ref_sparse_poly1 * __SPOL1ptr ; // std::vector<monome>: sparse 1-d poly (type _SPOL1)
      ref_string * __STRNGptr;
      size_t _FUNC_;
      // ref_unary_function_ptr * __FUNCptr;
      ref_gen_user * __USERptr;
      ref_gen_map * __MAPptr;
      ref_eqwdata * __EQWptr;
      ref_grob * __GROBptr;
      ref_void_pointer * __POINTERptr;
#endif
    };
    inline volatile ref_count_t & ref_count() const { 
#ifdef SMARTPTR64
      return ((ref_mpz_t *) ((* (ulonglong *) (this))>>16))->ref_count;
#else
      return __ZINTptr->ref_count;
#endif
    }
    gen(): type(_INT_),subtype(0),val(0) {
#ifdef COMPILE_FOR_STABILITY
      control_c();
#endif
    };
#ifdef SMARTPTR64
    gen(void *ptr,short int subt)  {
#ifdef COMPILE_FOR_STABILITY
      control_c();
#endif
      ulonglong __POINTERptr = (ulonglong ) new ref_void_pointer(ptr); 
#ifndef NO_STDEXCEPT
      if (__POINTERptr & 0xffff000000000000)
	setsizeerr(gettext("Pointer out of range"));
#endif
      * ((ulonglong *) this) = __POINTERptr << 16;
      subtype=(signed char)subt;
      type=_POINTER_;
    };
#else
    gen(void *ptr,short int subt): type(_POINTER_),subtype(char(subt)) {
#ifdef COMPILE_FOR_STABILITY
      control_c();
#endif
      __POINTERptr=new ref_void_pointer(ptr); 
    };
#endif
    gen(int i): type(_INT_),subtype(0),val(i) {
#ifdef COMPILE_FOR_STABILITY
      control_c();
#endif
    };
    gen(size_t i): type(_INT_),subtype(0),val((int)i)  {
#ifdef COMPILE_FOR_STABILITY
      control_c();
#endif
    };
    gen(long i);
    gen(longlong i);
    gen(longlong i,int nbits);
#ifdef INT128
    gen(int128_t i);
#endif
    gen(const mpz_t & m);
    // WARNING coerce *mptr to an int if possible, in this case delete mptr
    // Pls do not use this constructor unless you know exactly what you do!!
    gen(ref_mpz_t * mptr);
#ifdef DOUBLEVAL
    gen(double d): type(_DOUBLE_),_DOUBLE_val(d) {};
#else
    // may not work on ia64 with -O2
    gen(double d);
#endif
    gen(const giac_float & f);
#ifdef BCD
    gen(accurate_bcd_float * b);
#endif
    // inline
    double DOUBLE_val() const ;
    giac_float FLOAT_val() const ;
    gen(int a,int b);
    gen(double a,double b);
    gen(const gen & a,const gen & b);
    gen(const std::complex<double> & c);
    gen(const gen & e);
    gen (const identificateur & s);
    gen (ref_identificateur * sptr);
    gen (const vecteur & v,short int s=0);
    gen (ref_vecteur * vptr,short int s=0); 
    // vptr must be a pointer allocated by new, do not delete it explicitly
    gen (const symbolic & s);
    gen (ref_symbolic * sptr);
    gen (const gen_user & g);
    gen (ref_gen_user * sptr);
    gen (const real_object & g);
    gen (const real_interval & g);
    // Pls do not use this constructor unless you know exactly what you do
    gen (Tref_tensor<gen> * pptr);
    gen (const polynome & p);
    gen (const fraction & p);
    gen (const std::string & s,GIAC_CONTEXT);
    gen (const wchar_t * s,GIAC_CONTEXT);
    gen (const char * s,GIAC_CONTEXT){ type=0; *this=gen(std::string(s),contextptr); };
    gen (const sparse_poly1 & p);
    gen (const unary_function_ptr & f,int nargs=1);
    gen (const unary_function_ptr * f,int nargs=1);
    gen (const gen_map & m);
    gen (const eqwdata & );
    gen (const grob & );
#ifdef HAVE_GMPXX_H
    gen (const mpz_class &);
#endif
    gen (const my_mpz &);
    void delete_gen();
    ~gen(){ 
      if ( type>_DOUBLE_ && type!=_FLOAT_
#if !defined SMARTPTR64 // || defined STATIC_BUILTIN_LEXER_FUNCTIONS
	   && type!=_FUNC 
#endif
	   ){
	// optimization for ref_count access must be checked in multi-thread
	ref_count_t * rc=(ref_count_t *) & ref_count();
	if (*rc!=-1 && !--*rc){
	  delete_gen();
	}
      }
    }

    bool in_eval(int level,gen & evaled,const context * contextptr) const;
    gen eval(int level,const context * contextptr) const;
    // inline gen eval() const { return eval(DEFAULT_EVAL_LEVEL,context0); }
    bool in_evalf(int level,gen & evaled,const context * contextptr) const;
    gen evalf(int level,const context * contextptr) const;
    // inline gen evalf() const { return evalf(DEFAULT_EVAL_LEVEL,context0); }
    gen evalf_double(int level,const context * contextptr) const ;
    gen evalf2double(int level,const context * contextptr) const;
#if defined SMARTPTR64 
    gen & operator = (const gen & a){
      ulonglong al=*((ulonglong *) &a);
      unsigned char atype=al&0x1f;
      ulonglong tl=*((ulonglong *) this);
      // Copy before deleting because the target might be embedded in a
      // with a ptr_val.ref_count of a equals to 1
      // short int type_save=type; // short int subtype_save=subtype; 
      * ((ulonglong *) this) = al;
      if (atype>_DOUBLE_ && atype!=_FLOAT_ 
	  && (al >> 16)	){
	ref_count_t * rc=(ref_count_t *)& ((ref_mpz_t *)(al>>16) )->ref_count;
	if (*rc!=-1)
	  ++(*rc); // increase ref count
      }
      // Now we delete the target 
      if ( (tl &0x1f)>_DOUBLE_)
	delete_ptr( (signed char) ((tl&0xff00)>>8),(tl &0x1f),(ref_mpz_t *) (tl >> 16));
      return *this;
    }
    
#else // SMARTPTR64
    gen & operator = (const gen & a){
      register unsigned t=(type << _DECALAGE) | a.type;
      if (!t){
	subtype=a.subtype;
	val=a.val;
	return *this;
      }
      if (a.type>_DOUBLE_ && a.type!=_FLOAT_ 
	  && a.type!=_FUNC && a.__ZINTptr
	  ){
	ref_count_t * rc=(ref_count_t *)&a.ref_count();
	if (*rc!=-1)
	  ++(*rc); // increase ref count
      }
      // Copy before deleting because the target might be embedded in a
      // with a ptr_val.ref_count of a equals to 1
      short int type_save=type; // short int subtype_save=subtype; 
      ref_mpz_t * ptr_save = __ZINTptr;
#ifdef DOUBLEVAL
      _DOUBLE_val = a._DOUBLE_val;
      subtype=a.subtype;
#else
      * ((ulonglong *) this) = *((ulonglong * ) &a);
#endif
      __ZINTptr=a.__ZINTptr;
      type=a.type;
      // Now we delete the target 
      if ( type_save>_DOUBLE_ && type_save!=_FLOAT_
	   && type_save!=_FUNC 
	   )
	delete_ptr(subtype,type_save,ptr_save);
      return *this;
    }
#endif // SMARTPTR64
    int to_int() const ;
    double to_double(const context * contextptr) const;
    bool is_vector_of_size(size_t n) const;
    bool is_identificateur_with_name(const char * s) const;
    bool is_real(GIAC_CONTEXT) const ;
    bool is_cinteger() const ;
    bool is_integer() const ;
    bool is_constant() const;
    std::string print(GIAC_CONTEXT) const;
    inline const char * printcharptr(GIAC_CONTEXT) const { return print(contextptr).c_str(); };
    // if sptr==0, return length required, otherwise print at end of *sptr
    int sprint(std::string * sptr,GIAC_CONTEXT) const; 
    std::string print_universal(GIAC_CONTEXT) const;
    std::string print() const;
    inline const char * printcharptr() const { return print().c_str(); };
    wchar_t * wprint(GIAC_CONTEXT) const ; 
    // print then convert to a malloc-ated wchar_t *
    void modify(int i) { *this =gen(i); };
    const char * dbgprint() const; 
    void uncoerce() ;
    gen conj(GIAC_CONTEXT) const;
    gen re(GIAC_CONTEXT) const ;
    gen im(GIAC_CONTEXT) const ;
    gen inverse(GIAC_CONTEXT) const;
    gen squarenorm(GIAC_CONTEXT) const;
    int bindigits() const ;
    gen operator [] (int i) const ;
    gen operator [] (const gen & i) const;
    gen operator_at(int i,GIAC_CONTEXT) const;
    gen operator_at(const gen & i,GIAC_CONTEXT) const;
    // gen & operator [] (int i) ;
    // gen & operator [] (const gen & i) ;
    gen operator () (const gen & i,GIAC_CONTEXT) const;
    gen operator () (const gen & i,const gen & progname,GIAC_CONTEXT) const;
    bool islesscomplexthan(const gen & other) const;
    bool is_approx() const ; // true if double/real or cmplx with re/im
    int symb_size() const;
    gen change_subtype(int newsubtype);
    bool is_symb_of_sommet(const unary_function_ptr & u) const ;
    bool is_symb_of_sommet(const unary_function_ptr * u) const ;
    gen makegen(int i) const; // make a gen of same type as this with integer i
    // For compatibility with older versions
    inline mpz_t * ref_ZINTptr() const ;
    inline real_object * ref_REALptr() const ;
    inline gen * ref_CPLXptr() const ;
    inline identificateur * ref_IDNTptr() const ;
    inline symbolic * ref_SYMBptr() const ;
    inline gen * ref_MODptr () const ;
    inline Tfraction<gen> * ref_FRACptr() const ;
    inline gen * ref_EXTptr () const ;
    inline polynome * ref_POLYptr() const ;
    inline vecteur * ref_VECTptr() const ;
    inline sparse_poly1 * ref_SPOL1ptr() const ;
    inline std::string * ref_STRNGptr() const ;
    inline unary_function_ptr * ref_FUNCptr() const ;
    inline gen_user * ref_USERptr() const ;
    inline gen_map * ref_MAPptr() const ;
    inline eqwdata * ref_EQWptr() const ;
    inline grob * ref_GROBptr() const ;
    inline void * ref_POINTER_val() const ;
  };

  bool ref_mpz_t2gen(ref_mpz_t * mptr,gen & g); // return true if mptr used in g
  gen change_subtype(const gen &g,int newsubtype);
  gen genfromstring(const std::string & s);
  // pointer to an int describing display mode for complex numbers
  int * complex_display_ptr(const gen & g); 
  // value==0 to cartesian, 1 to polar, 2 toggle, 3 count complex
  // returns the number of complex
  int adjust_complex_display(gen & res,int value); 

#if defined(SMARTPTR64)
  typedef ulonglong alias_gen;
#else
  struct alias_gen {
    unsigned char type;  // see dispatch.h
    signed char subtype;
    unsigned short reserved; // not used 
#ifdef DOUBLEVAL
    longlong value;
#else
    long value ; 
#endif
  };
#endif

  class vectpoly:public std::vector<polynome> {
  public:
    vectpoly():std::vector<polynome>::vector() {};
    vectpoly(size_t i,const polynome & p):std::vector<polynome>::vector(i,p) {};
    const char * dbgprint(){  
#ifndef NSPIRE
      CERR << *this << std::endl; 
#endif
      return "Done";
    }
  };

  struct ref_gen_map {
    volatile ref_count_t ref_count;
    gen_map m;
#if 1 // def NSPIRE
    ref_gen_map(): ref_count(1),m() {}
#else
    ref_gen_map(const std::pointer_to_binary_function < const gen &, const gen &, bool> & p): ref_count(1),m(p) {}
#endif
    ref_gen_map(const gen_map & M):ref_count(1),m(M) {}
  };

  struct alias_ref_fraction { ref_count_t ref_count; alias_gen num; alias_gen den; };
  struct alias_ref_complex {
    ref_count_t ref_count;
    int display;
    alias_gen re,im;
  };

  struct ref_vecteur {
    volatile ref_count_t ref_count;
    vecteur v;
    ref_vecteur():ref_count(1) {}
    ref_vecteur(unsigned s):ref_count(1),v(s) {}
    ref_vecteur(unsigned s,const gen & g):ref_count(1),v(s,g) {}
    ref_vecteur(const_iterateur it,const_iterateur itend):ref_count(1),v(it,itend) {}
    ref_vecteur(const vecteur & w):ref_count(1),v(w) {}
  };


#ifdef SMARTPTR64
#define define_alias_gen(name,type,subtype,ptr) alias_gen name={(ulonglong(ptr) << 16) | (subtype << 8) | type };
#define define_alias_ref_symbolic(name,sommet,type,subtype,ptr) alias_ref_symbolic name={-1,(unary_function_eval *)sommet,(ulonglong(ptr) << 16) | (subtype << 8) | type};
#define define_alias_ref_fraction(name,numtype,numsubtype,numptr,dentype,densubtype,denptr) alias_ref_fraction name={-1,{(ulonglong(numptr) << 16) | (numsubtype << 8) | numtype },{(ulonglong(denptr) << 16) | (densubtype << 8) | dentype }};
#define define_alias_ref_complex(name,retype,resubtype,reptr,imtype,imsubtype,imptr) alias_ref_complex name={-1,0,{(ulonglong(reptr) << 16) | (resubtype << 8) | retype },{(ulonglong(imptr) << 16) | (imsubtype << 8) | imtype }};
#define define_tab2_alias_gen(name,retype,resubtype,reptr,imtype,imsubtype,imptr) alias_gen name[]={{(ulonglong(reptr) << 16) | (resubtype << 8) | retype },{(ulonglong(imptr) << 16) | (imsubtype << 8) | imtype }};
#else // SMARTPTR64
#ifdef DOUBLEVAL
#define define_alias_gen(name,type,subtype,ptr) alias_gen name={type,subtype,0,ulonglong(ptr)};
#define define_alias_ref_symbolic(name,sommet,type,subtype,ptr) alias_ref_symbolic name={-1,(unary_function_eval *)sommet,type,subtype,0,ulonglong(ptr)};
#define define_alias_ref_fraction(name,numtype,numsubtype,numptr,dentype,densubtype,denptr) alias_ref_fraction name={-1,{numtype,numsubtype,0,ulonglong(numptr)},{dentype,densubtype,0,ulonglong(denptr)}};
#define define_alias_ref_complex(name,retype,resubtype,reptr,imtype,imsubtype,imptr) alias_ref_complex name={-1,0,{retype,resubtype,0,ulonglong(reptr)},{imtype,imsubtype,0,ulonglong(imptr)}};
#define define_tab2_alias_gen(name,retype,resubtype,reptr,imtype,imsubtype,imptr) alias_gen name[]={{retype,resubtype,0,ulonglong(reptr)},{imtype,imsubtype,0,ulonglong(imptr)}};
#else // DOUBLEVAL
#define define_alias_gen(name,type,subtype,ptr) alias_gen name={type,subtype,0,long(ptr)};
#define define_alias_ref_symbolic(name,sommet,type,subtype,ptr) alias_ref_symbolic name={-1,(unary_function_eval *)sommet,type,subtype,0,long(ptr)};
#define define_alias_ref_fraction(name,numtype,numsubtype,numptr,dentype,densubtype,denptr) alias_ref_fraction name={-1,{numtype,numsubtype,0,long(numptr)},{dentype,densubtype,0,long(denptr)}};
#define define_alias_ref_complex(name,retype,resubtype,reptr,imtype,imsubtype,imptr) alias_ref_complex name={-1,0,{retype,resubtype,0,long(reptr)},{imtype,imsubtype,0,long(imptr)}};
#define define_tab2_alias_gen(name,retype,resubtype,reptr,imtype,imsubtype,imptr) alias_gen name[]={{retype,resubtype,0,long(reptr)},{imtype,imsubtype,0,long(imptr)}};
#endif // DOUBLEVAL
#endif // SMARTPTR64

  // ? #ifdef __GNUC__
#ifdef IMMEDIATE_VECTOR
  struct alias_ref_vecteur { ref_count_t ref_count; const int _taille; const alias_gen * begin_immediate_vect; const alias_gen * end_immediate_vect; void * ptr; };
#define define_alias_ref_vecteur(name,b) alias_ref_vecteur name={-1,sizeof(b)/sizeof(gen),(const alias_gen *)b,(const alias_gen *)b+sizeof(b)/sizeof(gen),0};
#define define_alias_ref_vecteur2(name,b) alias_ref_vecteur name={-1,2,&b[0],&b[2],0};
#else
  struct alias_ref_vecteur { ref_count_t ref_count; const alias_gen * begin; const alias_gen * end; const alias_gen * finish; void * ptr; };
#define define_alias_ref_vecteur(name,b) alias_ref_vecteur name={-1,(const alias_gen *)b,(const alias_gen *)b+sizeof(b)/sizeof(gen),(const alias_gen *)b+sizeof(b)/sizeof(gen),0};
#define define_alias_ref_vecteur2(name,b) alias_ref_vecteur name={-1,&b[0],&b[2],&b[2],0};
#endif

  struct ref_complex {
    volatile ref_count_t ref_count;
    int display;
    gen re,im;
    ref_complex(const gen & R,const gen & I):ref_count(1),display(0),re(R),im(I) {}
    ref_complex(const gen & R,const gen & I,int display_mode):ref_count(1),display(display_mode),re(R),im(I) {}
  };
  struct ref_modulo {
    volatile ref_count_t ref_count;
    gen n,modulo;
    ref_modulo():ref_count(1) {}
    ref_modulo(const gen &N,const gen &M):ref_count(1),n(N),modulo(M) {}
  };
  struct ref_algext {
    volatile ref_count_t ref_count;
    gen P,Pmin,additional;
    ref_algext():ref_count(1) {}
  };

  bool poly_is_real(const polynome & p);
  bool vect_is_real(const vecteur & v,GIAC_CONTEXT);
  polynome addpoly(const polynome & p,const gen & c);
  polynome subpoly(const polynome & p,const gen & c);
  bool islesscomplexthanf(const gen & a,const gen & b);
  void islesscomplexthanf_sort(iterateur it,iterateur itend);
  void gen_sort_f(iterateur it,iterateur itend,bool (*f)(const gen &a,const gen &b));
  void gen_sort_f_context(iterateur it,iterateur itend,bool (*f)(const gen &a,const gen &b,GIAC_CONTEXT),GIAC_CONTEXT);
  gen makemap(); // make a new map
  gen chartab2gen(char * & s,GIAC_CONTEXT);


  bool is_zero(const gen & a,GIAC_CONTEXT0);
  bool is_exactly_zero(const gen & a);
  bool is_one(const gen & a);
  bool is_minus_one(const gen & a);
  bool is_sq_minus_one(const gen & a);
  bool is_inf(const gen & e);
  bool is_undef(const gen & e);
  bool is_undef(const polynome & p);
  bool is_undef(const vecteur & v);
  bool has_inf_or_undef(const gen & g);
  bool is_undef(const sparse_poly1 & s);
  bool is_zero__VECT(const vecteur & a,GIAC_CONTEXT);
  bool has_denominator(const gen & n);
  bool has_i(const gen & g);

  // basic arithmetic
  gen operator && (const gen & a,const gen & b);
  gen operator || (const gen & a,const gen & b);
  gen operator_plus (const gen & a,const gen & b,GIAC_CONTEXT);
  gen operator + (const gen & a,const gen & b);
  gen & operator_plus_eq (gen & a,const gen & b,GIAC_CONTEXT);
  inline gen & operator += (gen & a,const gen & b){ 
    return operator_plus_eq(a,b,giac::context0);
  }
  Tfraction<gen> operator + (const Tfraction<gen> & a,const Tfraction<gen> & b); // specialization
  gen sym_add (const gen & a,const gen & b,GIAC_CONTEXT);
  gen & operator_minus_eq (gen & a,const gen & b,GIAC_CONTEXT);
  inline gen & operator -= (gen & a,const gen & b){ 
    return operator_minus_eq(a,b,giac::context0);
  }
  gen operator_minus (const gen & a,const gen & b,GIAC_CONTEXT);
  gen operator - (const gen & a,const gen & b);
  gen operator - (const gen & a);
  gen sym_sub (const gen & a,const gen & b,GIAC_CONTEXT);
  gen operator_times (const gen & a,const gen & b,GIAC_CONTEXT);
  gen operator * (const gen & a,const gen & b);
  inline gen operator * (int a,const gen & b){ return gen(a)*b; }
  inline gen operator * (double a,const gen & b){ return gen(a)*b; }
  gen sym_mult (const gen & a,const gen & b,GIAC_CONTEXT);
  gen pow(const gen & base,const gen & exponent,GIAC_CONTEXT);
  gen giac_pow(const gen & base,const gen & exponent,GIAC_CONTEXT);
  gen iquo(const gen & a,const gen & b); // same
  gen irem(const gen & a,const gen & b,gen & q); // same
  gen smod(const gen & a,const gen & b); // same
  void smod(const vecteur & v,const gen & g,vecteur & w); 
  vecteur smod(const vecteur & a,const gen & b); // same
  gen rdiv(const gen & a,const gen & b,GIAC_CONTEXT0); // rational division
  inline gen operator /(const gen & a,const gen & b){ return rdiv(a,b); };
  gen operator %(const gen & a,const gen & b); // for int only
  // gen inv(const gen & a);
  gen inv(const gen & a,GIAC_CONTEXT);
  inline wchar_t * wprint(const gen & g,GIAC_CONTEXT){ return g.wprint(contextptr); }

  inline void swapgen(gen & a,gen &b){
#ifdef SMARTPTR64
    std::swap<ulonglong>(* (ulonglong *)&a,* (ulonglong *)&b);
#else
    gen tmp=a; a=b; b=tmp;
#endif
  }
  gen algebraic_EXTension(const gen & a,const gen & v);
  gen ext_reduce(const gen & a, const gen & v);
  gen maptoarray(const gen_map & m,GIAC_CONTEXT);
  gen evalf_VECT(const vecteur & v,int subtype,int level,const context * contextptr);
  gen m_gamma(int nbits); // Euler gamma constant precision nbits
  gen m_gamma(GIAC_CONTEXT);
  gen m_pi(int nbits); // pi precision nbits
  gen m_pi(GIAC_CONTEXT);

  // a*b -> tmp, may modify tmp in place
  void type_operator_times(const gen & a,const gen &b,gen & tmp);
  // c += a*b, may modify c in place
  /*
  inline void type_operator_plus_times(const gen & a,const gen & b,gen & c){
    gen g;
    type_operator_times(a,b,g);
    c += g;
  }
  */
  void type_operator_plus_times(const gen & a,const gen & b,gen & c);
  void type_operator_minus_times(const gen & a,const gen & b,gen & c);

  inline void type_operator_plus_times_reduce(const gen & a,const gen & b,gen & c,int reduce){
    type_operator_plus_times(a,b,c);
    if (reduce)
      c=smod(c,reduce);
  }

  inline void type_operator_reduce(const gen & a,const gen & b,gen & c,int reduce){
    type_operator_times(a,b,c);
    if (reduce)
      c=smod(c,reduce);
  }

  bool operator ==(const gen & a,const gen & b);
  bool operator ==(const gen & a,const identificateur & b);
  bool operator_equal(const gen & a,const gen & b,GIAC_CONTEXT);
  bool operator !=(const gen & a,const gen & b);
  inline bool operator !=(const gen & a,const identificateur & b){ return !(a==b); }
  gen equal(const gen & a,const gen &b,GIAC_CONTEXT);
  gen equal2(const gen & a,const gen &b,GIAC_CONTEXT);

  gen operator !(const gen & a);

  int fastsign(const gen & a,GIAC_CONTEXT);   // 0 if unknown, 1 if >0, -1 if <0
  gen sign(const gen & a,GIAC_CONTEXT);

  // Large tests if strictly not precised, if sign is unknown return false 
  bool is_greater(const gen & a,const gen &b,GIAC_CONTEXT);
  bool is_strictly_greater(const gen & a,const gen &b,GIAC_CONTEXT);
  inline bool operator > (const gen & a,const gen & b){
    return is_strictly_greater(a,b,giac::context0);
  }
  bool is_positive(const gen & a,GIAC_CONTEXT);
  bool is_strictly_positive(const gen & a,GIAC_CONTEXT);
  // Large tests if strictly not precised, if sign is unknown make an error
  bool ck_is_greater(const gen & a,const gen &b,GIAC_CONTEXT);
  bool ck_is_strictly_greater(const gen & a,const gen &b,GIAC_CONTEXT);
  bool ck_is_positive(const gen & a,GIAC_CONTEXT);
  bool ck_is_strictly_positive(const gen & a,GIAC_CONTEXT);
  gen superieur_strict(const gen & a,const gen & b,GIAC_CONTEXT);
  gen superieur_egal(const gen & a,const gen & b,GIAC_CONTEXT);
  gen inferieur_strict(const gen & a,const gen & b,GIAC_CONTEXT);
  gen inferieur_egal(const gen & a,const gen & b,GIAC_CONTEXT);
  bool symb_size_less(const gen & a,const gen & b);

  gen min(const gen & a, const gen & b,GIAC_CONTEXT);
  gen max(const gen & a, const gen & b,GIAC_CONTEXT=context0);
  // default context0 is required for instantiation in poly.h
  gen factorial(unsigned long int i);
  gen comb(unsigned long int i,unsigned long j);
  gen perm(unsigned long int i,unsigned long j);
  gen pow(const gen & base, unsigned long int exponent);
  gen pow(const gen & base, int exponent);
  gen pow(unsigned long int base, unsigned long int exponent);

  // more advanced arithmetic
  gen gcd(const gen & A,const gen & B,GIAC_CONTEXT);
  gen gcd(const gen & A,const gen & B);
  gen lcm(const gen & a,const gen & b);
  gen simplify(gen & n, gen & d);
  void egcd(const gen &a,const gen &b, gen & u,gen &v,gen &d );
  gen ichinrem(const gen & a,const gen &b,const gen & amod, const gen & bmod);
  gen invmod(const gen & A,const gen & modulo);
  gen fracmod(const gen & a_orig,const gen & modulo); // -> p/q=a mod modulo
  bool fracmod(const gen & a_orig,const gen & modulo,gen & res);
  bool in_fracmod(const gen &m,const gen & a,mpz_t & d,mpz_t & d1,mpz_t & absd1,mpz_t &u,mpz_t & u1,mpz_t & ur,mpz_t & q,mpz_t & r,mpz_t &sqrtm,mpz_t & tmp,gen & num,gen & den);
  gen powmod(const gen &base,const gen & expo,const gen & modulo);
  gen isqrt(const gen & A);
  gen re(const gen & a,GIAC_CONTEXT);
  gen no_context_re(const gen & a);
  gen im(const gen & a,GIAC_CONTEXT);
  gen no_context_im(const gen & a);
  void reim(const gen & g,gen & r,gen & i,GIAC_CONTEXT);
  gen conj(const gen & a,GIAC_CONTEXT);
  gen no_context_conj(const gen & a);
  gen sq(const gen & a);
  gen abs(const gen & a,const context * contextptr=context0);
  // default context0 is required for instantiation in poly.h
  gen linfnorm(const gen & a,const context * contextptr=context0);
  // default context0 is required for instantiation in poly.h
  gen arg(const gen & a,GIAC_CONTEXT);
  gen arg_CPLX(const gen & a,GIAC_CONTEXT);
  int is_perfect_square(const gen & A);
  int is_probab_prime_p(const gen & A);
  gen nextprime(const gen & a); // more precisely next probably prime
  gen prevprime(const gen & a); // more precisely prev probably prime
  int jacobi(const gen & A, const gen &B);
  int legendre(const gen & A, const gen & B);
  vecteur pascal_next_line(const vecteur & v); 
  vecteur pascal_nth_line(int n);
  // convert a __VECTOR__VECT vecteur to a normal vecteur
  gen vector2vecteur(const vecteur & v);

  // if b is a _MOD, returns a as a b _MOD 
  gen chkmod(const gen& a,const gen & b);
  // make a _MOD a%b
  gen makemod(const gen & a,const gen & b);
  // same without evaluating %
  gen makemodquoted(const gen & a,const gen & b);

  // from a sum in x returns a list of [coeff monomial]
  // e.g. 5+2x+3*x*y -> [ [5 1] [2 x] [ 3 x*y] ]
  vecteur symbolique2liste(const gen & x,GIAC_CONTEXT);
  // v should be sorted and shrinked
  gen liste2symbolique(const vecteur & v);

  bool is_atomic(const gen & e);
  gen _FRAC2_SYMB(const fraction & f);
  gen _FRAC2_SYMB(const gen & e);
  gen _FRAC2_SYMB(const gen & n,const gen & d);
  gen string2gen(const std::string & ss,bool remove_ss_quotes=true);
  // by default ss is assumed to be delimited by " and "
  std::complex<double> gen2complex_d(const gen & e);
  gen eval_VECT(const vecteur & v,int subtype,int level,const context * context_ptr );
  // functional equivalent of gen methods
  inline gen eval(const gen & e,int level,const context * contextptr){ return e.eval(level,contextptr); };
  inline gen eval(const gen & e,const context * contextptr){ return e.eval(eval_level(contextptr),contextptr); };
  gen no_context_evalf(const gen & e);
  gen evalf(const gen & e,int level,const context * contextptr );
  gen evalf2bcd_nock(const gen & g0,int level,const context * contextptr);
  gen evalf2bcd(const gen & g0,int level,const context * contextptr);
  inline gen evalf_double(const gen & e,int level,const context * contextptr){ return e.evalf_double(level,contextptr); };
  // return true if g can be converted to a double or real or complex
  bool has_evalf(const gen & g,gen & res,int level,const context * contextptr);
  inline std::string print(const gen & e,context * contextptr){ return e.print(contextptr); }
  inline bool is_real(const gen & g,GIAC_CONTEXT){ return g.is_real(contextptr); }
  inline  bool is_cinteger(const gen & g){ return g.is_cinteger();}  ;
  inline  bool is_integer(const gen & g){ return g.is_integer(); }  ;
  double int2double(int i);
  inline  bool is_constant(const gen & g){ return g.is_constant(); } ;
  inline bool is_approx(const gen & g){ return g.is_approx(); };
  gen aplatir_fois_plus(const gen & g);
  gen collect(const gen & g,GIAC_CONTEXT);

  class gen_user{
  public:
    virtual gen_user * memory_alloc() const { gen_user * ptr = new gen_user(*this); return ptr; }
    virtual ~gen_user() {}; 
    // redefine operations if it makes sense. 
    // You can redefine gen_user + gen_user for speed
    virtual gen operator + (const gen &) const { return gensizeerr(gettext("+ not redefined")); }
    virtual gen operator + (const gen_user & a) const { return (*this) + gen(a); }
    virtual gen operator - (const gen &) const { return gensizeerr(gettext("Binary - not redefined")); }
    virtual gen operator - (const gen_user & a) const { return (*this) - gen(a); }
    virtual gen operator - () const { return gensizeerr(gettext("Unary - not redefined")); }
    virtual gen operator * (const gen &) const { return gensizeerr(gettext("Binary * not redefined")); }
    virtual gen operator * (const gen_user & a) const { return (*this) * gen(a); }
    virtual gen operator / (const gen_user & a) const { return (*this) * a.inv(); }
    virtual gen operator / (const gen & a) const { return gensizeerr(gettext("Binary / not redefined")); }
    virtual bool is_zero() const { 
#ifndef NO_STDEXCEPT
      setsizeerr(gettext("==0 not redefined")); 
#endif
      return false;
    }
    virtual bool is_one() const { 
#ifndef NO_STDEXCEPT
      setsizeerr(gettext("==1 not redefined")); 
#endif
      return false;
    }
    virtual bool is_minus_one() const { 
#ifndef NO_STDEXCEPT
      setsizeerr(gettext("==-1 not redefined")); 
#endif
      return false;
    }
    virtual gen inv() const { return gensizeerr(gettext("Inv not redefined")); }
    virtual gen conj(GIAC_CONTEXT) const { return gensizeerr(gettext("Conj not redefined"));}
    virtual gen re(GIAC_CONTEXT) const { return gensizeerr(gettext("Real part not redefined"));}
    virtual gen im(GIAC_CONTEXT) const { return gensizeerr(gettext("Imaginary part not redefined")); }
    virtual gen abs(GIAC_CONTEXT) const { return gensizeerr(gettext("Abs not redefined"));}
    virtual gen arg(GIAC_CONTEXT) const { return gensizeerr(gettext("Arg not redefined")); }
    virtual gen sqrt(GIAC_CONTEXT) const { return gensizeerr(gettext("Sqrt not redefined")); }
    virtual gen operator () (const gen &,GIAC_CONTEXT) const { return gensizeerr(gettext("() not redefined")); }
    virtual gen operator [] (const gen &) { return gensizeerr(gettext("[] not redefined")); }
    virtual bool operator == (const gen &) const { 
#ifndef NO_STDEXCEPT
      setsizeerr(gettext("== not redefined")); 
#endif
      return false;
    }
    virtual bool operator == (const gen_user & a) const { return (*this) == gen(a); }
    // must redefine > AND <= since we do not have symetrical type arguments
    virtual gen operator > (const gen &) const { return gensizeerr(gettext("> not redefined")); }
    virtual gen operator > (const gen_user & a) const { return superieur_strict(*this, gen(a),0); }
    virtual gen operator <= (const gen &) const { return gensizeerr(gettext("<= not redefined")); }
    virtual gen operator <= (const gen_user & a) const { return inferieur_egal(*this, gen(a),0); }
    virtual gen polygcd (const polynome &,const polynome &,polynome &) const { return gensizeerr(gettext("Polynomial gcd not redefined")); }    
    virtual gen polyfactor (const polynome & p,
			     factorization & f) const { 
      return gensizeerr(gettext("Polynomial gcd not redefined")); 
    }    
    virtual gen gcd (const gen &) const { return gensizeerr(gettext("gcd not redefined")); }    
    virtual gen gcd (const gen_user & a) const { return gcd(gen(a)); }
    virtual std::string print (GIAC_CONTEXT) const { return  "Nothing_to_print";}
    const char * dbgprint () const { 
      static std::string s;
      s=this->print(0);
#ifndef NSPIRE
      CERR << s << std::endl;
#endif
      return s.c_str();
    }
    virtual std::string texprint (GIAC_CONTEXT) const { return "Nothing_to_print_tex"; }
    virtual gen eval(int level,const context * contextptr) const {return *this;};
    virtual gen evalf(int level,const context * contextptr) const {return *this;};
    virtual gen makegen(int i) const { return string2gen("makegen not redefined"); } ;
    virtual gen rand(GIAC_CONTEXT) const { return string2gen("rand not redefined"); };
  };
  struct ref_gen_user {
    volatile ref_count_t ref_count;
    gen_user * u;
    ref_gen_user(const gen_user & U):ref_count(1),u(U.memory_alloc()) {}
    ref_gen_user(gen_user * U):ref_count(1),u(U) {}
    ~ref_gen_user() {delete u;}
  };

  std::string print_the_type(int val,GIAC_CONTEXT);

  // I/O
#ifdef NSPIRE
  template<class T> nio::ios_base<T> & operator<<(nio::ios_base<T> & os,const gen & a){
    return os << a.print(context0); 
  }
  template<class T> nio::ios_base<T> & operator>>(nio::ios_base<T> & is,gen & a);
#else
  std::ostream & operator << (std::ostream & os,const gen & a);
  std::istream & operator >> (std::istream & is,gen & a);
#endif

#if defined(GIAC_GENERIC_CONSTANTS) // || (defined(VISUALC) && !defined(RTOS_THREADX)) || defined(x86_64)
  extern const gen zero;
#else
  extern const gen & zero;
#endif

  struct monome {
    gen coeff;
    gen exponent;
    monome():coeff(0),exponent(0) {};
    monome(const gen & mycoeff) : coeff(mycoeff),exponent(zero) {};
    monome(const gen &mycoeff,const gen &myexponent) : coeff(mycoeff),exponent(myexponent) {};
    // std::string print() const ;
    std::string print(GIAC_CONTEXT) const ;
    const char * dbgprint() const ;
  };
#ifdef NSPIRE
  template<class T> nio::ios_base<T> & operator<<(nio::ios_base<T> & os,const monome & m){    return os << m.print() ;}
#else
  std::ostream & operator << (std::ostream & os,const monome & m);
#endif
  inline bool operator == (const monome & a,const monome & b){ return a.coeff==b.coeff && a.exponent==b.exponent; }
  inline bool operator != (const monome & a,const monome & b){ return a.coeff!=b.coeff || a.exponent!=b.exponent; }
  polynome apply( const polynome & p, const context * contextptr, gen (* f) (const gen &, const context *));
  
  const char * printi(GIAC_CONTEXT);
  std::string hexa_print_ZINT(const mpz_t & a);
  std::string octal_print_ZINT(const mpz_t & a);
  std::string binary_print_ZINT(const mpz_t & a);
  std::string print_ZINT(const mpz_t & a);
  std::string printinner_VECT(const vecteur & v, int subtype,GIAC_CONTEXT);
  std::string & add_printinner_VECT(std::string & s,const vecteur &v,int subtype,GIAC_CONTEXT);
  std::string begin_VECT_string(int subtype,bool tex,GIAC_CONTEXT);
  std::string end_VECT_string(int subtype,bool tex,GIAC_CONTEXT);
  std::string print_VECT(const vecteur & v,int subtype,GIAC_CONTEXT); // subtype was 0 by default
  std::string print_SPOL1(const sparse_poly1 & p,GIAC_CONTEXT);
  std::string print_STRNG(const std::string & s);
  std::string printint32(int val,int subtype,GIAC_CONTEXT);
  std::string print_FLOAT_(const giac_float & f,GIAC_CONTEXT);
  // find closing or opening () [] {}
  bool matchpos(const std::string & s,int & pos);
  std::string cut_string(const std::string & chaine,int nchar,std::vector<int> & ligne_end) ;
  std::string calc_endlines_positions(const vecteur & history_in,const vecteur & history_out,int nchar,std::vector<int> & endlines,std::vector<int> & positions);
  bool is_operator_char(char c);
  void increase_selection(const std::string & s,int & pos1,int& pos2);
  void decrease_selection(const std::string & s,int & pos1,int& pos2);
  void move_selection_right(const std::string & s,int & pos1, int & pos2);
  void move_selection_left(const std::string & s,int & pos1, int & pos2);
  std::string remove_extension(const std::string & chaine);


  // This type collects global variables to enable threading
  struct environment {
    gen modulo; // characteristic
    bool moduloon; // Set to false if non modular arithmetic required
    bool complexe; // true if working on Z/pZ[i]
    gen pn; // cardinal of the field, 0 means equal to modulo
    gen coeff; // exemple of coeff, so that we can call coeff.makegen
    environment(){
      modulo=13;
      moduloon=false;
      complexe=false;
      coeff=pn=0;
    }
  };

    struct ref_sparse_poly1 {
    volatile ref_count_t ref_count;
    sparse_poly1 s;
    ref_sparse_poly1(const sparse_poly1 & S):ref_count(1),s(S) {}
  };
  

  // extern environment * env; 

  struct attributs {
    int fontsize;
    int background;
    int text_color;
    attributs(int f,int b,int t): fontsize(f),background(b),text_color(t) {};
    attributs():fontsize(0),background(0),text_color(0) {};
  };

  // Terminal data for EQW display
  struct eqwdata {
    gen g; 
    attributs eqw_attributs;
    int x,y,dx,dy;
    bool selected;
    bool active;
    bool hasbaseline;
    bool modifiable;
    int baseline;
    eqwdata(int dxx,int dyy,int xx, int yy,const attributs & a,const gen& gg):g(gg),eqw_attributs(a),x(xx),y(yy),dx(dxx),dy(dyy),selected(false),active(false),hasbaseline(false),modifiable(true),baseline(0) {};
    eqwdata(int dxx,int dyy,int xx, int yy,const attributs & a,const gen& gg,int mybaseline):g(gg),eqw_attributs(a),x(xx),y(yy),dx(dxx),dy(dyy),selected(false),active(false),hasbaseline(true),modifiable(true),baseline(mybaseline) {};
    const char * dbgprint(){ 
#ifndef NSPIRE
      CERR << g << ":" << dx<< ","<< dy<< "+"<<x <<","<< y<< "," << baseline << "," << eqw_attributs.fontsize << "," << eqw_attributs.background << "," << eqw_attributs.text_color << std::endl; 
#endif
      return "Done";
    }
  };
  struct ref_eqwdata {
    volatile ref_count_t ref_count;
    eqwdata e;
    ref_eqwdata(const eqwdata & E): ref_count(1),e(E) {}
  };


  class identificateur {
  public:
    int * ref_count;
    gen * value;
    // std::string * name;
    const char * id_name;
    vecteur * localvalue;
    // value / localvalue might be an assumption if it's a vecteur 
    // of subtype _ASSUME__VECT
    // The first gen of an assumption vecteur is the type (_FRAC for rational)
    // If the type is _REAL, the vecteur has 2 other elements
    // * an interval or a _SET_VECT of intervals 
    //   where interval=vecteur of length 2 of subtype _LINE__VECT
    // * a list of excluded particular values
    // If the type is _DOUBLE_ the variable will be evalf-ed but not eval-ed
    // This is useful in geometry to make figures and get exact results
    // If the type is _INT_ it 
    short int * quoted;
    identificateur();
    explicit identificateur(const std::string & s);
    explicit identificateur(const char * s);
#ifdef GIAC_HAS_STO_38
    explicit identificateur(const char * s, bool StringIsNowYours); // creates identifier. if StringIsNowYours, then the string will be freed when id is destroyed...
#endif
    explicit identificateur(const char * s,const gen & e);
    identificateur(const std::string & s,const gen & e);
    identificateur(const identificateur & s);
    ~identificateur();
    identificateur & operator =(const identificateur & s);
    gen eval(int level,const gen & orig,const context * context_ptr) ;
    bool in_eval(int level,const gen & orig,gen & evaled,const context * context_ptr, bool No38Lookup=false); // if No38Lookup, does not check if HP38 knows about this name...
    const char * print(const context * context_ptr) const ;
    std::string name() const { return id_name; }
    const char * dbgprint() const { 
      static std::string s;
      s=this->print(context0); 
#if 0 // ndef NSPIRE
      COUT << s;
#endif
      return s.c_str();
    }
    void unassign() ;
    void push(int protection,const gen & e);
    bool operator ==(const identificateur & i);
    bool operator ==(const gen & i);
    inline bool operator !=(const identificateur & i){ return !(*this==i); }
    inline bool operator !=(const gen & i){ return !(*this==i);}
    void MakeCopyOfNameIfNotLocal(); ///< if the name is not dynamicaly allocated, create a copy for that id.
  };
  struct ref_identificateur {
    volatile ref_count_t ref_count;
    identificateur i;
    ref_identificateur(const char * s):ref_count(1),i(s){}
    ref_identificateur(const std::string & s):ref_count(1),i(s){}
    ref_identificateur(const identificateur & s):ref_count(1),i(s){}
  };
  struct alias_ref_identificateur {
    ref_count_t i;
    int * ref_count;
    gen * value;
    const char * id_name;
    vecteur * localvalue;
    short int * quoted;
  };

  struct ref_unary_function_ptr {
    volatile ref_count_t ref_count;
    unary_function_ptr u;
    ref_unary_function_ptr(const unary_function_ptr & U):ref_count(1),u(U) {}
    ref_unary_function_ptr(const unary_function_ptr * U):ref_count(1),u(*U) {}
  };
  struct symbolic {
    unary_function_ptr sommet; 
    gen feuille;
    symbolic(const unary_function_ptr & o,const gen & e): sommet(o),feuille(e){};
    symbolic(const unary_function_ptr & o,const gen & e1,const gen &e2): sommet(o), feuille(makevecteur(e1,e2)) {};
    symbolic(const unary_function_ptr & o,const gen & e1,const gen &e2,const gen & e3): sommet(o), feuille(makevecteur(e1,e2,e3)) {};
    symbolic(const unary_function_ptr & o,const gen & e1,const gen &e2,const gen & e3,const gen & e4): sommet(o), feuille(makevecteur(e1,e2,e3,e4)) {};
    symbolic(const unary_function_ptr * o,const gen & e): sommet(*o),feuille(e){};
    symbolic(const unary_function_ptr * o,const gen & e1,const gen &e2): sommet(*o), feuille(makevecteur(e1,e2)) {};
    symbolic(const unary_function_ptr * o,const gen & e1,const gen &e2,const gen & e3): sommet(*o), feuille(makevecteur(e1,e2,e3)) {};
    symbolic(const unary_function_ptr * o,const gen & e1,const gen &e2,const gen & e3,const gen & e4): sommet(*o), feuille(makevecteur(e1,e2,e3,e4)) {};
    symbolic(const symbolic & mys) : sommet(mys.sommet),feuille(mys.feuille) {};
    symbolic(const symbolic & mys,const gen & e);
    symbolic(const gen & a,const unary_function_ptr & o,const gen & b);
    symbolic(const gen & a,const unary_function_ptr * o,const gen & b);
    std::string print(GIAC_CONTEXT) const;
    const char * dbgprint() const { 
      static std::string s;
      s=this->print(context0);
#if 0 // ndef NSPIRE
      COUT << s << std::endl; 
#endif
      return s.c_str();
    }
    gen eval(int level,const context * context_ptr) const;
    gen evalf(int level,const context * context_ptr) const;
    int size() const;
  };

  struct ref_symbolic {
    volatile ref_count_t ref_count;
    symbolic s;
    ref_symbolic(const symbolic & S):ref_count(1),s(S) {}
  };
#ifdef SMARTPTR64
  struct alias_ref_symbolic {
    ref_count_t ref_count;
    unary_function_eval * sommet;
    ulonglong feuille;
  };
#else
  struct alias_ref_symbolic {
    ref_count_t ref_count;
    unary_function_eval * sommet;
    unsigned char type;  // see dispatch.h
    signed char subtype;
    unsigned short reserved; // not used 
#ifdef DOUBLEVAL
    longlong value;
#else
    long value ; 
#endif
  };
#endif

#ifdef SMARTPTR64
  inline mpz_t * gen::ref_ZINTptr() const { return & ((ref_mpz_t *) (* (ulonglong *) this >> 16))->z ; }
  inline real_object * gen::ref_REALptr() const { return & ((ref_real_object *) (* (ulonglong *) this >> 16)) ->r; }
  inline gen * gen::ref_CPLXptr() const { return & ((ref_complex *)(* (ulonglong *) this >> 16))->re; }
  inline gen * gen::ref_MODptr () const { return & ((ref_modulo *)(* (ulonglong *) this >> 16))->n; }
  inline gen * gen::ref_EXTptr () const { return & ((ref_algext *)(* (ulonglong *) this >> 16))->P; }
  inline vecteur * gen::ref_VECTptr() const { return &((ref_vecteur*)(* (ulonglong *) this >> 16))->v; }
  inline sparse_poly1 * gen::ref_SPOL1ptr() const { return &((ref_sparse_poly1*)(* (ulonglong *) this >> 16))->s; }
  inline std::string * gen::ref_STRNGptr() const { return &((ref_string*)(* (ulonglong *) this >> 16))->s; }
  inline gen_user * gen::ref_USERptr() const { return ((ref_gen_user*)(* (ulonglong *) this >> 16))->u; }
  inline gen_map * gen::ref_MAPptr() const { return &((ref_gen_map*)(* (ulonglong *) this >> 16))->m; }
  inline eqwdata * gen::ref_EQWptr() const { return &((ref_eqwdata*)(* (ulonglong *) this >> 16))->e; }
  inline grob * gen::ref_GROBptr() const { return &((ref_grob*)(* (ulonglong *) this >> 16))->g; }
  inline void * gen::ref_POINTER_val() const { return ((ref_void_pointer*)(* (ulonglong *) this >> 16))->p; }
  inline Tfraction<gen> * gen::ref_FRACptr() const { return &((ref_fraction *)(* (ulonglong *) this >> 16))->f; }
  inline polynome * gen::ref_POLYptr() const { return &((ref_polynome*)(* (ulonglong *) this >> 16))->t; }
  inline identificateur * gen::ref_IDNTptr() const {return &((ref_identificateur*)(* (ulonglong *) this >> 16))->i; }
  inline symbolic * gen::ref_SYMBptr() const { return &((ref_symbolic*)(* (ulonglong *) this >> 16))->s; }
  inline unary_function_ptr * gen::ref_FUNCptr() const { return &((ref_unary_function_ptr*)(* (ulonglong *) this >> 16))->u; }
#else // SMARTPTR64
  inline mpz_t * gen::ref_ZINTptr() const { return &__ZINTptr->z; }
  inline real_object * gen::ref_REALptr() const { return &__REALptr->r; }
  inline gen * gen::ref_CPLXptr() const { return &__CPLXptr->re; }
  inline gen * gen::ref_MODptr () const { return &__MODptr->n; }
  inline gen * gen::ref_EXTptr () const { return &__EXTptr->P; }
  inline vecteur * gen::ref_VECTptr() const { return &__VECTptr->v; }
  inline sparse_poly1 * gen::ref_SPOL1ptr() const { return &__SPOL1ptr->s; }
  inline std::string * gen::ref_STRNGptr() const { return &__STRNGptr->s; }
  inline gen_user * gen::ref_USERptr() const { return __USERptr->u; }
  inline gen_map * gen::ref_MAPptr() const { return &__MAPptr->m; }
  inline eqwdata * gen::ref_EQWptr() const { return &__EQWptr->e; }
  inline grob * gen::ref_GROBptr() const { return &__GROBptr->g; }
  inline void * gen::ref_POINTER_val() const { return __POINTERptr->p; }
  inline Tfraction<gen> * gen::ref_FRACptr() const { return &__FRACptr->f; }
  inline polynome * gen::ref_POLYptr() const { return &__POLYptr->t; }
  inline identificateur * gen::ref_IDNTptr() const {return &__IDNTptr->i; }
  inline symbolic * gen::ref_SYMBptr() const { return &__SYMBptr->s; }
  // inline unary_function_ptr * gen::ref_FUNCptr() const { return &__FUNCptr->u; }
  inline unary_function_ptr * gen::ref_FUNCptr() const { return (unary_function_ptr*) &_FUNC_; }
#endif // SMARTPTR64

#ifndef DOUBLEVAL
#define _DOUBLE_val DOUBLE_val()
#define _FLOAT_val FLOAT_val()
#endif // DOUBLEVAL
#define  _ZINTptr ref_ZINTptr()
#define	 _REALptr ref_REALptr()
#define  _CPLXptr ref_CPLXptr()
#define  _IDNTptr ref_IDNTptr()
#define  _SYMBptr ref_SYMBptr()
#define  _MODptr ref_MODptr()
#define  _FRACptr ref_FRACptr()
#define  _EXTptr ref_EXTptr()
#define  _POLYptr ref_POLYptr ()
#define  _VECTptr  ref_VECTptr()
#define  _SPOL1ptr ref_SPOL1ptr()
#define  _STRNGptr ref_STRNGptr()
#define  _FUNCptr ref_FUNCptr()
#define  _ROOTptr ref_ROOTptr()
#define  _USERptr ref_USERptr()
#define  _MAPptr ref_MAPptr()
#define  _EQWptr ref_EQWptr()
#define  _GROBptr ref_GROBptr()
#define  _POINTER_val ref_POINTER_val()

  // function that are indexed
  extern const alias_type alias_at_plus;
  extern const alias_type alias_at_neg;
  extern const alias_type alias_at_binary_minus;
  extern const alias_type alias_at_prod;
  extern const alias_type alias_at_division;
  extern const alias_type alias_at_inv;
  extern const alias_type alias_at_pow;
  extern const alias_type alias_at_exp;
  extern const alias_type alias_at_ln;
  extern const alias_type alias_at_abs;
  extern const alias_type alias_at_arg;
  extern const alias_type alias_at_pnt;
  extern const alias_type alias_at_point;
  extern const alias_type alias_at_segment;
  extern const alias_type alias_at_sto;
  extern const alias_type alias_at_sin;
  extern const alias_type alias_at_cos;
  extern const alias_type alias_at_tan;
  extern const alias_type alias_at_asin;
  extern const alias_type alias_at_acos;
  extern const alias_type alias_at_atan;
  extern const alias_type alias_at_sinh;
  extern const alias_type alias_at_cosh;
  extern const alias_type alias_at_tanh;
  extern const alias_type alias_at_asinh;
  extern const alias_type alias_at_acosh;
  extern const alias_type alias_at_atanh;
  extern const alias_type alias_at_interval;
  extern const alias_type alias_at_union;
  extern const alias_type alias_at_minus;
  extern const alias_type alias_at_intersect;
  extern const alias_type alias_at_not;
  extern const alias_type alias_at_and;
  extern const alias_type alias_at_ou;
  extern const alias_type alias_at_inferieur_strict;
  extern const alias_type alias_at_inferieur_egal;
  extern const alias_type alias_at_superieur_strict;
  extern const alias_type alias_at_superieur_egal;
  extern const alias_type alias_at_different;
  extern const alias_type alias_at_equal;
  extern const alias_type alias_at_equal2;
  extern const alias_type alias_at_rpn_prog;
  extern const alias_type alias_at_local;
  extern const alias_type alias_at_return;
  extern const alias_type alias_at_Dialog;
  extern const alias_type alias_at_double_deux_points;
  extern const alias_type alias_at_pointprod;
  extern const alias_type alias_at_pointdivision;
  extern const alias_type alias_at_pointpow;
  extern const alias_type alias_at_hash;
  extern const alias_type alias_at_pourcent;
  extern const alias_type alias_at_tilocal;
  extern const alias_type alias_at_break;
  extern const alias_type alias_at_continue;
  extern const alias_type alias_at_ampersand_times;
  extern const alias_type alias_at_maple_lib;
  extern const alias_type alias_at_unit;
  extern const alias_type alias_at_plot_style;
  extern const alias_type alias_at_xor;
  extern const alias_type alias_at_check_type;
  extern const alias_type alias_at_quote_pow;
  extern const alias_type alias_at_case;
  extern const alias_type alias_at_dollar;
  extern const alias_type alias_at_IFTE;
  extern const alias_type alias_at_RPN_CASE;
  extern const alias_type alias_at_RPN_LOCAL;
  extern const alias_type alias_at_RPN_FOR;
  extern const alias_type alias_at_RPN_WHILE;
  extern const alias_type alias_at_NOP;
  extern const alias_type alias_at_unit;
  extern const alias_type alias_at_ifte;
  extern const alias_type alias_at_for;
  extern const alias_type alias_at_bloc;
  extern const alias_type alias_at_program;
  extern const alias_type alias_at_same;
  extern const alias_type alias_at_increment;
  extern const alias_type alias_at_decrement;
  extern const alias_type alias_at_multcrement;
  extern const alias_type alias_at_divcrement;
  extern const alias_type alias_at_sq;
  extern const alias_type alias_at_display;
  extern const alias_type alias_at_of;
  extern const alias_type alias_at_at;
  extern const alias_type alias_at_normalmod;  
  extern const alias_type alias_at_pointplus;
  extern const alias_type alias_at_pointminus;

#ifdef BCD
  inline bool ck_gentobcd(const gen & g,accurate_bcd_float * bcdptr){
    if (g.type!=_FLOAT_)
      return false;
    fExpand(g._FLOAT_val.f,bcdptr);
    return true;
  }
  inline accurate_bcd_float * gentobcd(const gen & g,accurate_bcd_float * bcdptr){
    return fExpand(g._FLOAT_val.f,bcdptr);
  }
#endif

  // should be in input_lexer.h
  // return true/false to tell if s is recognized. return the appropriate gen if true
  bool CasIsBuildInFunction(char const *s, gen &g);

  void sprintfdouble(char *,const char *,double d);

  extern "C" const char * caseval(const char *);

#ifndef NO_NAMESPACE_GIAC
} // namespace giac
#endif // ndef NO_NAMESPACE_GIAC

#endif // _GIAC_GEN_H