numeric.h

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/*
 *  GiNaC Copyright (C) 1999-2011 Johannes Gutenberg University Mainz, Germany
 *
 *  This program is free software; you can redistribute it and/or modify
 *  it under the terms of the GNU General Public License as published by
 *  the Free Software Foundation; either version 2 of the License, or
 *  (at your option) any later version.
 *
 *  This program is distributed in the hope that it will be useful,
 *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 *  GNU General Public License for more details.
 *
 *  You should have received a copy of the GNU General Public License
 *  along with this program; if not, write to the Free Software
 *  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
 */

#ifndef GINAC_NUMERIC_H
#define GINAC_NUMERIC_H

#include "basic.h"
#include "ex.h"
#include "archive.h"

#include <cln/complex.h>
#if defined(G__CINTVERSION) && !defined(__MAKECINT__)
// Cint @$#$! doesn't like forward declaring classes used for casting operators
// so we have to include the definition of cln::cl_N here, but it is enough to
// do so for the compiler, hence the !defined(__MAKECINT__).
  #include <cln/complex_class.h>
#endif
#include <stdexcept>
#include <vector>

namespace GiNaC {

typedef void (* digits_changed_callback)(long);

class _numeric_digits
{
// member functions
public:
    _numeric_digits();
    _numeric_digits& operator=(long prec);
    operator long();
    void print(std::ostream& os) const;
    void add_callback(digits_changed_callback callback);
// member variables
private:
    long digits;                        
    static bool too_late;               
    // Holds a list of functions that get called when digits is changed.
    std::vector<digits_changed_callback> callbacklist;
};


class pole_error : public std::domain_error {
public:
    explicit pole_error(const std::string& what_arg, int degree);
    int degree() const;
private:
    int deg;
};


class numeric : public basic
{
    GINAC_DECLARE_REGISTERED_CLASS(numeric, basic)
    
// member functions
    
    // other constructors
public:
    numeric(int i);
    numeric(unsigned int i);
    numeric(long i);
    numeric(unsigned long i);
    numeric(long numer, long denom);
    numeric(double d);
    numeric(const char *);
    
    // functions overriding virtual functions from base classes
public:
    unsigned precedence() const {return 30;}
    bool info(unsigned inf) const;
    bool is_polynomial(const ex & var) const;
    int degree(const ex & s) const;
    int ldegree(const ex & s) const;
    ex coeff(const ex & s, int n = 1) const;
    bool has(const ex &other, unsigned options = 0) const;
    ex eval(int level = 0) const;
    ex evalf(int level = 0) const;
    ex subs(const exmap & m, unsigned options = 0) const { return subs_one_level(m, options); } // overwrites basic::subs() for performance reasons
    ex normal(exmap & repl, exmap & rev_lookup, int level = 0) const;
    ex to_rational(exmap & repl) const;
    ex to_polynomial(exmap & repl) const;
    numeric integer_content() const;
    ex smod(const numeric &xi) const;
    numeric max_coefficient() const;
    ex conjugate() const;
    ex real_part() const;
    ex imag_part() const;
    void archive(archive_node& n) const;
    void read_archive(const archive_node& n, lst& syms);
protected:
    ex derivative(const symbol &s) const { return 0; }
    bool is_equal_same_type(const basic &other) const;
    unsigned calchash() const;
    
    // new virtual functions which can be overridden by derived classes
    // (none)
    
    // non-virtual functions in this class
public:
    const numeric add(const numeric &other) const;
    const numeric sub(const numeric &other) const;
    const numeric mul(const numeric &other) const;
    const numeric div(const numeric &other) const;
    const numeric power(const numeric &other) const;
    const numeric & add_dyn(const numeric &other) const;
    const numeric & sub_dyn(const numeric &other) const;
    const numeric & mul_dyn(const numeric &other) const;
    const numeric & div_dyn(const numeric &other) const;
    const numeric & power_dyn(const numeric &other) const;
    const numeric & operator=(int i);
    const numeric & operator=(unsigned int i);
    const numeric & operator=(long i);
    const numeric & operator=(unsigned long i);
    const numeric & operator=(double d);
    const numeric & operator=(const char *s);
    const numeric inverse() const;
    numeric step() const;
    int csgn() const;
    int compare(const numeric &other) const;
    bool is_equal(const numeric &other) const;
    bool is_zero() const;
    bool is_positive() const;
    bool is_negative() const;
    bool is_integer() const;
    bool is_pos_integer() const;
    bool is_nonneg_integer() const;
    bool is_even() const;
    bool is_odd() const;
    bool is_prime() const;
    bool is_rational() const;
    bool is_real() const;
    bool is_cinteger() const;
    bool is_crational() const;
    bool operator==(const numeric &other) const;
    bool operator!=(const numeric &other) const;
    bool operator<(const numeric &other) const;
    bool operator<=(const numeric &other) const;
    bool operator>(const numeric &other) const;
    bool operator>=(const numeric &other) const;
    int to_int() const;
    long to_long() const;
    double to_double() const;
    cln::cl_N to_cl_N() const;
    const numeric real() const;
    const numeric imag() const;
    const numeric numer() const;
    const numeric denom() const;
    int int_length() const;
    // converting routines for interfacing with CLN:
    explicit numeric(const cln::cl_N &z);

protected:
    void print_numeric(const print_context & c, const char *par_open, const char *par_close, const char *imag_sym, const char *mul_sym, unsigned level) const;
    void do_print(const print_context & c, unsigned level) const;
    void do_print_latex(const print_latex & c, unsigned level) const;
    void do_print_csrc(const print_csrc & c, unsigned level) const;
    void do_print_csrc_cl_N(const print_csrc_cl_N & c, unsigned level) const;
    void do_print_tree(const print_tree & c, unsigned level) const;
    void do_print_python_repr(const print_python_repr & c, unsigned level) const;

// member variables

protected:
    cln::cl_N value;
};
GINAC_DECLARE_UNARCHIVER(numeric); 


// global constants

extern const numeric I;
extern _numeric_digits Digits;

// global functions

const numeric exp(const numeric &x);
const numeric log(const numeric &x);
const numeric sin(const numeric &x);
const numeric cos(const numeric &x);
const numeric tan(const numeric &x);
const numeric asin(const numeric &x);
const numeric acos(const numeric &x);
const numeric atan(const numeric &x);
const numeric atan(const numeric &y, const numeric &x);
const numeric sinh(const numeric &x);
const numeric cosh(const numeric &x);
const numeric tanh(const numeric &x);
const numeric asinh(const numeric &x);
const numeric acosh(const numeric &x);
const numeric atanh(const numeric &x);
const numeric Li2(const numeric &x);
const numeric zeta(const numeric &x);
const numeric lgamma(const numeric &x);
const numeric tgamma(const numeric &x);
const numeric psi(const numeric &x);
const numeric psi(const numeric &n, const numeric &x);
const numeric factorial(const numeric &n);
const numeric doublefactorial(const numeric &n);
const numeric binomial(const numeric &n, const numeric &k);
const numeric bernoulli(const numeric &n);
const numeric fibonacci(const numeric &n);
const numeric isqrt(const numeric &x);
const numeric sqrt(const numeric &x);
const numeric abs(const numeric &x);
const numeric mod(const numeric &a, const numeric &b);
const numeric smod(const numeric &a, const numeric &b);
const numeric irem(const numeric &a, const numeric &b);
const numeric irem(const numeric &a, const numeric &b, numeric &q);
const numeric iquo(const numeric &a, const numeric &b);
const numeric iquo(const numeric &a, const numeric &b, numeric &r);
const numeric gcd(const numeric &a, const numeric &b);
const numeric lcm(const numeric &a, const numeric &b);

// wrapper functions around member functions
inline const numeric pow(const numeric &x, const numeric &y)
{ return x.power(y); }

inline const numeric inverse(const numeric &x)
{ return x.inverse(); }

inline numeric step(const numeric &x)
{ return x.step(); }

inline int csgn(const numeric &x)
{ return x.csgn(); }

inline bool is_zero(const numeric &x)
{ return x.is_zero(); }

inline bool is_positive(const numeric &x)
{ return x.is_positive(); }

inline bool is_negative(const numeric &x)
{ return x.is_negative(); }

inline bool is_integer(const numeric &x)
{ return x.is_integer(); }

inline bool is_pos_integer(const numeric &x)
{ return x.is_pos_integer(); }

inline bool is_nonneg_integer(const numeric &x)
{ return x.is_nonneg_integer(); }

inline bool is_even(const numeric &x)
{ return x.is_even(); }

inline bool is_odd(const numeric &x)
{ return x.is_odd(); }

inline bool is_prime(const numeric &x)
{ return x.is_prime(); }

inline bool is_rational(const numeric &x)
{ return x.is_rational(); }

inline bool is_real(const numeric &x)
{ return x.is_real(); }

inline bool is_cinteger(const numeric &x)
{ return x.is_cinteger(); }

inline bool is_crational(const numeric &x)
{ return x.is_crational(); }

inline int to_int(const numeric &x)
{ return x.to_int(); }

inline long to_long(const numeric &x)
{ return x.to_long(); }

inline double to_double(const numeric &x)
{ return x.to_double(); }

inline const numeric real(const numeric &x)
{ return x.real(); }

inline const numeric imag(const numeric &x)
{ return x.imag(); }

inline const numeric numer(const numeric &x)
{ return x.numer(); }

inline const numeric denom(const numeric &x)
{ return x.denom(); }

// numeric evaluation functions for class constant objects:

ex PiEvalf();
ex EulerEvalf();
ex CatalanEvalf();


} // namespace GiNaC

#ifdef __MAKECINT__
#pragma link off defined_in cln/number.h;
#pragma link off defined_in cln/complex_class.h;
#endif

#endif // ndef GINAC_NUMERIC_H