GiNaC/ginac/numeric.h

/** @file numeric.h
 *
 *  Makes the interface to the underlying bignum package available. */

/*
 *  GiNaC Copyright (C) 1999-2001 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., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 */

#ifndef __GINAC_NUMERIC_H__
#define __GINAC_NUMERIC_H__

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

#include <cln/number.h>
// forward decln of cln::cl_N, since cln/complex_class.h is not included:
namespace cln { class cl_N; }

#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

namespace GiNaC {

/** 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;
// member variables
private:
        long digits;                        ///< Number of decimal digits
        static bool too_late;               ///< Already one object present
};

/** 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 ctors
public:
        explicit numeric(int i);
        explicit numeric(unsigned int i);
        explicit numeric(long i);
        explicit numeric(unsigned long i);
        explicit numeric(long numer, long denom);
        explicit numeric(double d);
        explicit numeric(const char *);
        
        // functions overriding virtual functions from bases classes
public:
        void print(const print_context & c, unsigned level = 0) const;
        unsigned precedence(void) const {return 30;}
        bool info(unsigned inf) const;
        bool has(const ex &other) const;
        ex eval(int level = 0) const;
        ex evalf(int level = 0) const;
        ex normal(lst &sym_lst, lst &repl_lst, int level = 0) const;
        ex to_rational(lst &repl_lst) const;
        numeric integer_content(void) const;
        ex smod(const numeric &xi) const;
        numeric max_coefficient(void) const;
protected:
        /** Implementation of ex::diff for a numeric always returns 0.
         *  @see ex::diff */
        ex derivative(const symbol &s) const { return _ex0(); }
        bool is_equal_same_type(const basic &other) const;
        unsigned calchash(void) 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(void) const;
        int csgn(void) const;
        int compare(const numeric &other) const;
        bool is_equal(const numeric &other) const;
        bool is_zero(void) const;
        bool is_positive(void) const;
        bool is_negative(void) const;
        bool is_integer(void) const;
        bool is_pos_integer(void) const;
        bool is_nonneg_integer(void) const;
        bool is_even(void) const;
        bool is_odd(void) const;
        bool is_prime(void) const;
        bool is_rational(void) const;
        bool is_real(void) const;
        bool is_cinteger(void) const;
        bool is_crational(void) 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(void) const;
        long to_long(void) const;
        double to_double(void) const;
        cln::cl_N to_cl_N(void) const;
        const numeric real(void) const;
        const numeric imag(void) const;
        const numeric numer(void) const;
        const numeric denom(void) const;
        int int_length(void) const;
        // converting routines for interfacing with CLN:
        numeric(const cln::cl_N &z);

// member variables

protected:
        cln::cl_number value;
};

// global constants

extern const numeric I;
extern _numeric_digits Digits;

// deprecated macro, for internal use only
#define is_a_numeric_hash(x) ((x)&0x80000000U)

// 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 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(void);
ex EulerEvalf(void);
ex CatalanEvalf(void);


// utility functions

/** Return the numeric object handled by an ex.  Deprecated: use ex_to<numeric>().
 *  This is unsafe: you need to check the type first. */
inline const numeric &ex_to_numeric(const ex &e)
{
        return static_cast<const numeric &>(*e.bp);
}

/** Specialization of is_exactly_a<numeric>(obj) for numeric objects. */
template<> inline bool is_exactly_a<numeric>(const basic & obj)
{
        return obj.tinfo()==TINFO_numeric;
}

} // 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__
1	cbauer	1.1	/** @file numeric.h
2			*
3	cbauer	1.4	* Makes the interface to the underlying bignum package available. */
4
5			/*
6	kreckel	1.43	* GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
7	cbauer	1.2	*
8			* This program is free software; you can redistribute it and/or modify
9			* it under the terms of the GNU General Public License as published by
10			* the Free Software Foundation; either version 2 of the License, or
11			* (at your option) any later version.
12			*
13			* This program is distributed in the hope that it will be useful,
14			* but WITHOUT ANY WARRANTY; without even the implied warranty of
15			* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
16			* GNU General Public License for more details.
17			*
18			* You should have received a copy of the GNU General Public License
19			* along with this program; if not, write to the Free Software
20			* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
21			*/
22	cbauer	1.1
23	cbauer	1.2	#ifndef __GINAC_NUMERIC_H__
24			#define __GINAC_NUMERIC_H__
25	cbauer	1.1
26	cbauer	1.21	#include "basic.h"
27			#include "ex.h"
28	cbauer	1.1
29	kreckel	1.41	#include <cln/number.h>
30			// forward decln of cln::cl_N, since cln/complex_class.h is not included:
31			namespace cln { class cl_N; }
32
33			#if defined(G__CINTVERSION) && !defined(__MAKECINT__)
34			// Cint @$#$! doesn't like forward declaring classes used for casting operators
35			// so we have to include the definition of cln::cl_N here, but it is enough to
36			// do so for the compiler, hence the !defined(__MAKECINT__).
37			#include <cln/complex_class.h>
38			#endif
39	cbauer	1.1
40	cbauer	1.5	namespace GiNaC {
41
42	kreckel	1.48	/** This class is used to instantiate a global singleton object Digits
43			* which behaves just like Maple's Digits. We need an object rather
44			* than a dumber basic type since as a side-effect we let it change
45	cbauer	1.1	* cl_default_float_format when it gets changed. The only other
46			* meaningful thing to do with it is converting it to an unsigned,
47			* for temprary storing its value e.g. The user must not create an
48			* own working object of this class! Since C++ forces us to make the
49			* class definition visible in order to use an object we put in a
50			* flag which prevents other objects of that class to be created. */
51			class _numeric_digits
52			{
53			// member functions
54			public:
55	cbauer	1.38	_numeric_digits();
56			_numeric_digits& operator=(long prec);
57			operator long();
58	kreckel	1.48	void print(std::ostream &os) const;
59	cbauer	1.1	// member variables
60			private:
61	kreckel	1.48	long digits; ///< Number of decimal digits
62			static bool too_late; ///< Already one object present
63	cbauer	1.1	};
64
65			/** This class is a wrapper around CLN-numbers within the GiNaC class
66			* hierarchy. Objects of this type may directly be created by the user.*/
67			class numeric : public basic
68			{
69	cbauer	1.38	GINAC_DECLARE_REGISTERED_CLASS(numeric, basic)
70	kreckel	1.48
71	cbauer	1.1	// member functions
72	kreckel	1.48
73			// other ctors
74	cbauer	1.1	public:
75	cbauer	1.38	explicit numeric(int i);
76			explicit numeric(unsigned int i);
77			explicit numeric(long i);
78			explicit numeric(unsigned long i);
79			explicit numeric(long numer, long denom);
80			explicit numeric(double d);
81			explicit numeric(const char *);
82
83			// functions overriding virtual functions from bases classes
84	cbauer	1.1	public:
85	cbauer	1.49	void print(const print_context & c, unsigned level = 0) const;
86	cbauer	1.51	unsigned precedence(void) const {return 30;}
87	cbauer	1.38	bool info(unsigned inf) const;
88	kreckel	1.48	bool has(const ex &other) const;
89	kreckel	1.47	ex eval(int level = 0) const;
90			ex evalf(int level = 0) const;
91	kreckel	1.48	ex normal(lst &sym_lst, lst &repl_lst, int level = 0) const;
92	cbauer	1.38	ex to_rational(lst &repl_lst) const;
93			numeric integer_content(void) const;
94			ex smod(const numeric &xi) const;
95			numeric max_coefficient(void) const;
96	cbauer	1.1	protected:
97	kreckel	1.48	/** Implementation of ex::diff for a numeric always returns 0.
98			* @see ex::diff */
99			ex derivative(const symbol &s) const { return _ex0(); }
100			bool is_equal_same_type(const basic &other) const;
101	cbauer	1.38	unsigned calchash(void) const;
102	kreckel	1.48
103	cbauer	1.38	// new virtual functions which can be overridden by derived classes
104			// (none)
105	kreckel	1.48
106	cbauer	1.38	// non-virtual functions in this class
107	cbauer	1.1	public:
108	kreckel	1.48	const numeric add(const numeric &other) const;
109			const numeric sub(const numeric &other) const;
110			const numeric mul(const numeric &other) const;
111			const numeric div(const numeric &other) const;
112			const numeric power(const numeric &other) const;
113			const numeric & add_dyn(const numeric &other) const;
114			const numeric & sub_dyn(const numeric &other) const;
115			const numeric & mul_dyn(const numeric &other) const;
116			const numeric & div_dyn(const numeric &other) const;
117			const numeric & power_dyn(const numeric &other) const;
118	cbauer	1.38	const numeric & operator=(int i);
119			const numeric & operator=(unsigned int i);
120			const numeric & operator=(long i);
121			const numeric & operator=(unsigned long i);
122			const numeric & operator=(double d);
123	kreckel	1.48	const numeric & operator=(const char *s);
124	kreckel	1.41	const numeric inverse(void) const;
125	cbauer	1.38	int csgn(void) const;
126	kreckel	1.48	int compare(const numeric &other) const;
127			bool is_equal(const numeric &other) const;
128	cbauer	1.38	bool is_zero(void) const;
129			bool is_positive(void) const;
130			bool is_negative(void) const;
131			bool is_integer(void) const;
132			bool is_pos_integer(void) const;
133			bool is_nonneg_integer(void) const;
134			bool is_even(void) const;
135			bool is_odd(void) const;
136			bool is_prime(void) const;
137			bool is_rational(void) const;
138			bool is_real(void) const;
139			bool is_cinteger(void) const;
140			bool is_crational(void) const;
141	kreckel	1.48	bool operator==(const numeric &other) const;
142			bool operator!=(const numeric &other) const;
143			bool operator<(const numeric &other) const;
144			bool operator<=(const numeric &other) const;
145			bool operator>(const numeric &other) const;
146			bool operator>=(const numeric &other) const;
147	cbauer	1.38	int to_int(void) const;
148			long to_long(void) const;
149			double to_double(void) const;
150	kreckel	1.42	cln::cl_N to_cl_N(void) const;
151	cbauer	1.38	const numeric real(void) const;
152			const numeric imag(void) const;
153			const numeric numer(void) const;
154			const numeric denom(void) const;
155			int int_length(void) const;
156	kreckel	1.41	// converting routines for interfacing with CLN:
157	kreckel	1.48	numeric(const cln::cl_N &z);
158	cbauer	1.1
159			// member variables
160
161			protected:
162	kreckel	1.41	cln::cl_number value;
163	cbauer	1.1	};
164
165			// global constants
166
167			extern const numeric I;
168			extern _numeric_digits Digits;
169
170	kreckel	1.48	// deprecated macro, for internal use only
171			#define is_a_numeric_hash(x) ((x)&0x80000000U)
172	cbauer	1.1
173			// global functions
174
175	kreckel	1.48	const numeric exp(const numeric &x);
176			const numeric log(const numeric &x);
177			const numeric sin(const numeric &x);
178			const numeric cos(const numeric &x);
179			const numeric tan(const numeric &x);
180			const numeric asin(const numeric &x);
181			const numeric acos(const numeric &x);
182			const numeric atan(const numeric &x);
183			const numeric atan(const numeric &y, const numeric &x);
184			const numeric sinh(const numeric &x);
185			const numeric cosh(const numeric &x);
186			const numeric tanh(const numeric &x);
187			const numeric asinh(const numeric &x);
188			const numeric acosh(const numeric &x);
189			const numeric atanh(const numeric &x);
190			const numeric Li2(const numeric &x);
191			const numeric zeta(const numeric &x);
192			const numeric lgamma(const numeric &x);
193			const numeric tgamma(const numeric &x);
194			const numeric psi(const numeric &x);
195			const numeric psi(const numeric &n, const numeric &x);
196			const numeric factorial(const numeric &n);
197			const numeric doublefactorial(const numeric &n);
198			const numeric binomial(const numeric &n, const numeric &k);
199			const numeric bernoulli(const numeric &n);
200			const numeric fibonacci(const numeric &n);
201			const numeric isqrt(const numeric &x);
202			const numeric sqrt(const numeric &x);
203			const numeric abs(const numeric &x);
204			const numeric mod(const numeric &a, const numeric &b);
205			const numeric smod(const numeric &a, const numeric &b);
206			const numeric irem(const numeric &a, const numeric &b);
207			const numeric irem(const numeric &a, const numeric &b, numeric &q);
208			const numeric iquo(const numeric &a, const numeric &b);
209			const numeric iquo(const numeric &a, const numeric &b, numeric &r);
210			const numeric gcd(const numeric &a, const numeric &b);
211			const numeric lcm(const numeric &a, const numeric &b);
212	cbauer	1.1
213			// wrapper functions around member functions
214	kreckel	1.48	inline const numeric pow(const numeric &x, const numeric &y)
215	kreckel	1.16	{ return x.power(y); }
216
217	kreckel	1.48	inline const numeric inverse(const numeric &x)
218	cbauer	1.1	{ return x.inverse(); }
219	kreckel	1.6
220	kreckel	1.48	inline int csgn(const numeric &x)
221	kreckel	1.6	{ return x.csgn(); }
222	cbauer	1.1
223	kreckel	1.48	inline bool is_zero(const numeric &x)
224	cbauer	1.1	{ return x.is_zero(); }
225
226	kreckel	1.48	inline bool is_positive(const numeric &x)
227	cbauer	1.1	{ return x.is_positive(); }
228
229	kreckel	1.48	inline bool is_integer(const numeric &x)
230	cbauer	1.1	{ return x.is_integer(); }
231
232	kreckel	1.48	inline bool is_pos_integer(const numeric &x)
233	cbauer	1.1	{ return x.is_pos_integer(); }
234
235	kreckel	1.48	inline bool is_nonneg_integer(const numeric &x)
236	cbauer	1.1	{ return x.is_nonneg_integer(); }
237
238	kreckel	1.48	inline bool is_even(const numeric &x)
239	cbauer	1.1	{ return x.is_even(); }
240
241	kreckel	1.48	inline bool is_odd(const numeric &x)
242	cbauer	1.1	{ return x.is_odd(); }
243
244	kreckel	1.48	inline bool is_prime(const numeric &x)
245	cbauer	1.1	{ return x.is_prime(); }
246
247	kreckel	1.48	inline bool is_rational(const numeric &x)
248	cbauer	1.1	{ return x.is_rational(); }
249
250	kreckel	1.48	inline bool is_real(const numeric &x)
251	cbauer	1.1	{ return x.is_real(); }
252
253	kreckel	1.48	inline bool is_cinteger(const numeric &x)
254	kreckel	1.14	{ return x.is_cinteger(); }
255
256	kreckel	1.48	inline bool is_crational(const numeric &x)
257	kreckel	1.14	{ return x.is_crational(); }
258	kreckel	1.42
259	kreckel	1.48	inline int to_int(const numeric &x)
260	kreckel	1.42	{ return x.to_int(); }
261
262	kreckel	1.48	inline long to_long(const numeric &x)
263	kreckel	1.42	{ return x.to_long(); }
264
265	kreckel	1.48	inline double to_double(const numeric &x)
266	kreckel	1.42	{ return x.to_double(); }
267	kreckel	1.14
268	kreckel	1.48	inline const numeric real(const numeric &x)
269	cbauer	1.1	{ return x.real(); }
270
271	kreckel	1.48	inline const numeric imag(const numeric &x)
272	cbauer	1.1	{ return x.imag(); }
273
274	kreckel	1.48	inline const numeric numer(const numeric &x)
275	cbauer	1.1	{ return x.numer(); }
276
277	kreckel	1.48	inline const numeric denom(const numeric &x)
278	cbauer	1.1	{ return x.denom(); }
279
280	kreckel	1.11	// numeric evaluation functions for class constant objects:
281
282	cbauer	1.1	ex PiEvalf(void);
283	kreckel	1.31	ex EulerEvalf(void);
284	cbauer	1.1	ex CatalanEvalf(void);
285
286	kreckel	1.23
287	cbauer	1.5	// utility functions
288	kreckel	1.54
289	kreckel	1.55	/** Return the numeric object handled by an ex. Deprecated: use ex_to<numeric>().
290	kreckel	1.54	* This is unsafe: you need to check the type first. */
291	kreckel	1.23	inline const numeric &ex_to_numeric(const ex &e)
292			{
293	cbauer	1.38	return static_cast<const numeric &>(*e.bp);
294	kreckel	1.54	}
295
296			/** Specialization of is_exactly_a<numeric>(obj) for numeric objects. */
297			template<> inline bool is_exactly_a<numeric>(const basic & obj)
298			{
299			return obj.tinfo()==TINFO_numeric;
300	kreckel	1.23	}
301
302	cbauer	1.5	} // namespace GiNaC
303	kreckel	1.41
304			#ifdef __MAKECINT__
305			#pragma link off defined_in cln/number.h;
306			#pragma link off defined_in cln/complex_class.h;
307			#endif
308	cbauer	1.1
309	cbauer	1.2	#endif // ndef __GINAC_NUMERIC_H__
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