/** @file numeric.h * * Makes the interface to the underlying bignum package available. */ /* * GiNaC Copyright (C) 1999-2006 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 #include #include #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 #endif namespace GiNaC { /** Function pointer to implement callbacks in the case 'Digits' gets changed. * Main purpose of such callbacks is to adjust look-up tables of certain * functions to the new precision. Parameter contains the signed difference * between new Digits and old Digits. */ typedef void (* digits_changed_callback)(long); /** This class is used to instantiate a global singleton object Digits * which behaves just like Maple's Digits. We need an object rather * than a dumber basic type since as a side-effect we let it change * cl_default_float_format when it gets changed. The only other * meaningful thing to do with it is converting it to an unsigned, * for temprary storing its value e.g. The user must not create an * own working object of this class! Since C++ forces us to make the * class definition visible in order to use an object we put in a * flag which prevents other objects of that class to be created. */ 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; ///< Number of decimal digits static bool too_late; ///< Already one object present // Holds a list of functions that get called when digits is changed. std::vector callbacklist; }; /** Exception class thrown when a singularity is encountered. */ class pole_error : public std::domain_error { public: explicit pole_error(const std::string& what_arg, int degree); int degree() const; private: int deg; }; /** This class is a wrapper around CLN-numbers within the GiNaC class * hierarchy. Objects of this type may directly be created by the user.*/ 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; 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; protected: /** Implementation of ex::diff for a numeric always returns 0. * @see ex::diff */ 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; int 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: 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; }; // 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 int 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_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__