GiNaC/ginac/numeric.h

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

/*
 *  GiNaC Copyright (C) 1999-2000 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 <strstream>
#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

#ifndef NO_NAMESPACE_GINAC
namespace GiNaC {
#endif // ndef NO_NAMESPACE_GINAC

#define HASHVALUE_NUMERIC 0x80000001U

/** This class is used to instantiate a global 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;
        static bool too_late;
};

/** 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)

// friends
// (none)

// member functions

        // default constructor, destructor, copy constructor assignment
        // operator and helpers
public:
        numeric();
        ~numeric();
        numeric(const numeric & other);
        const numeric & operator=(const numeric & other);
protected:
        void copy(const numeric & other);
        void destroy(bool call_parent);

        // other constructors
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:
        basic * duplicate() const;
        void print(std::ostream & os, unsigned precedence=0) const;
        void printraw(std::ostream & os) const;
        void printtree(std::ostream & os, unsigned indent) const;
        void printcsrc(std::ostream & os, unsigned type, unsigned precedence=0) const;
        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:
        ex derivative(const symbol & s) const;
        int compare_same_type(const basic & other) const;
        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:
        static unsigned precedence;
        cln::cl_number value;
};

// global constants

extern const numeric some_numeric;
extern const numeric I;
extern const std::type_info & typeid_numeric;
extern _numeric_digits Digits;

//#define is_a_numeric_hash(x) ((x)==HASHVALUE_NUMERIC)
// may have to be changed to ((x)>=0x80000000U)

// has been changed
//#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 abs(const numeric & x);
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
inline const numeric &ex_to_numeric(const ex &e)
{
        return static_cast<const numeric &>(*e.bp);
}


#ifndef NO_NAMESPACE_GINAC
} // namespace GiNaC
#endif // ndef NO_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	1.17	* GiNaC Copyright (C) 1999-2000 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			#include <strstream>
27	cbauer	1.21	#include "basic.h"
28			#include "ex.h"
29	cbauer	1.1
30	kreckel	1.41	#include <cln/number.h>
31			// forward decln of cln::cl_N, since cln/complex_class.h is not included:
32			namespace cln { class cl_N; }
33
34			#if defined(G__CINTVERSION) && !defined(__MAKECINT__)
35			// Cint @$#$! doesn't like forward declaring classes used for casting operators
36			// so we have to include the definition of cln::cl_N here, but it is enough to
37			// do so for the compiler, hence the !defined(__MAKECINT__).
38			#include <cln/complex_class.h>
39			#endif
40	cbauer	1.1
41	kreckel	1.22	#ifndef NO_NAMESPACE_GINAC
42	cbauer	1.5	namespace GiNaC {
43	kreckel	1.22	#endif // ndef NO_NAMESPACE_GINAC
44	cbauer	1.5
45			#define HASHVALUE_NUMERIC 0x80000001U
46
47	cbauer	1.1	/** This class is used to instantiate a global object Digits which
48			* behaves just like Maple's Digits. We need an object rather than a
49			* dumber basic type since as a side-effect we let it change
50			* cl_default_float_format when it gets changed. The only other
51			* meaningful thing to do with it is converting it to an unsigned,
52			* for temprary storing its value e.g. The user must not create an
53			* own working object of this class! Since C++ forces us to make the
54			* class definition visible in order to use an object we put in a
55			* flag which prevents other objects of that class to be created. */
56			class _numeric_digits
57			{
58			// member functions
59			public:
60	cbauer	1.38	_numeric_digits();
61			_numeric_digits& operator=(long prec);
62			operator long();
63			void print(std::ostream & os) const;
64	cbauer	1.1	// member variables
65			private:
66	cbauer	1.38	long digits;
67			static bool too_late;
68	cbauer	1.1	};
69
70			/** This class is a wrapper around CLN-numbers within the GiNaC class
71			* hierarchy. Objects of this type may directly be created by the user.*/
72			class numeric : public basic
73			{
74	cbauer	1.38	GINAC_DECLARE_REGISTERED_CLASS(numeric, basic)
75	cbauer	1.18
76	cbauer	1.1	// friends
77	kreckel	1.41	// (none)
78	cbauer	1.1
79			// member functions
80
81	cbauer	1.38	// default constructor, destructor, copy constructor assignment
82			// operator and helpers
83	cbauer	1.1	public:
84	cbauer	1.38	numeric();
85			~numeric();
86			numeric(const numeric & other);
87			const numeric & operator=(const numeric & other);
88	cbauer	1.1	protected:
89	cbauer	1.38	void copy(const numeric & other);
90			void destroy(bool call_parent);
91	cbauer	1.1
92	cbauer	1.38	// other constructors
93	cbauer	1.1	public:
94	cbauer	1.38	explicit numeric(int i);
95			explicit numeric(unsigned int i);
96			explicit numeric(long i);
97			explicit numeric(unsigned long i);
98			explicit numeric(long numer, long denom);
99			explicit numeric(double d);
100			explicit numeric(const char *);
101
102			// functions overriding virtual functions from bases classes
103	cbauer	1.1	public:
104	cbauer	1.38	basic * duplicate() const;
105			void print(std::ostream & os, unsigned precedence=0) const;
106			void printraw(std::ostream & os) const;
107			void printtree(std::ostream & os, unsigned indent) const;
108			void printcsrc(std::ostream & os, unsigned type, unsigned precedence=0) const;
109			bool info(unsigned inf) const;
110			bool has(const ex & other) const;
111			ex eval(int level=0) const;
112			ex evalf(int level=0) const;
113			ex normal(lst &sym_lst, lst &repl_lst, int level=0) const;
114			ex to_rational(lst &repl_lst) const;
115			numeric integer_content(void) const;
116			ex smod(const numeric &xi) const;
117			numeric max_coefficient(void) const;
118	cbauer	1.1	protected:
119	cbauer	1.38	ex derivative(const symbol & s) const;
120			int compare_same_type(const basic & other) const;
121			bool is_equal_same_type(const basic & other) const;
122			unsigned calchash(void) const;
123	cbauer	1.1
124	cbauer	1.38	// new virtual functions which can be overridden by derived classes
125			// (none)
126	cbauer	1.1
127	cbauer	1.38	// non-virtual functions in this class
128	cbauer	1.1	public:
129	kreckel	1.41	const numeric add(const numeric & other) const;
130			const numeric sub(const numeric & other) const;
131			const numeric mul(const numeric & other) const;
132			const numeric div(const numeric & other) const;
133			const numeric power(const numeric & other) const;
134	cbauer	1.38	const numeric & add_dyn(const numeric & other) const;
135			const numeric & sub_dyn(const numeric & other) const;
136			const numeric & mul_dyn(const numeric & other) const;
137			const numeric & div_dyn(const numeric & other) const;
138			const numeric & power_dyn(const numeric & other) const;
139			const numeric & operator=(int i);
140			const numeric & operator=(unsigned int i);
141			const numeric & operator=(long i);
142			const numeric & operator=(unsigned long i);
143			const numeric & operator=(double d);
144			const numeric & operator=(const char * s);
145	kreckel	1.41	const numeric inverse(void) const;
146	cbauer	1.38	int csgn(void) const;
147			int compare(const numeric & other) const;
148			bool is_equal(const numeric & other) const;
149			bool is_zero(void) const;
150			bool is_positive(void) const;
151			bool is_negative(void) const;
152			bool is_integer(void) const;
153			bool is_pos_integer(void) const;
154			bool is_nonneg_integer(void) const;
155			bool is_even(void) const;
156			bool is_odd(void) const;
157			bool is_prime(void) const;
158			bool is_rational(void) const;
159			bool is_real(void) const;
160			bool is_cinteger(void) const;
161			bool is_crational(void) const;
162			bool operator==(const numeric & other) const;
163			bool operator!=(const numeric & other) const;
164			bool operator<(const numeric & other) const;
165			bool operator<=(const numeric & other) const;
166			bool operator>(const numeric & other) const;
167			bool operator>=(const numeric & other) const;
168			int to_int(void) const;
169			long to_long(void) const;
170			double to_double(void) const;
171	kreckel	1.42	cln::cl_N to_cl_N(void) const;
172	cbauer	1.38	const numeric real(void) const;
173			const numeric imag(void) const;
174			const numeric numer(void) const;
175			const numeric denom(void) const;
176			int int_length(void) const;
177	kreckel	1.41	// converting routines for interfacing with CLN:
178			numeric(const cln::cl_N & z);
179	cbauer	1.1
180			// member variables
181
182			protected:
183	cbauer	1.38	static unsigned precedence;
184	kreckel	1.41	cln::cl_number value;
185	cbauer	1.1	};
186
187			// global constants
188
189			extern const numeric some_numeric;
190			extern const numeric I;
191	kreckel	1.40	extern const std::type_info & typeid_numeric;
192	cbauer	1.1	extern _numeric_digits Digits;
193
194	frink	1.26	//#define is_a_numeric_hash(x) ((x)==HASHVALUE_NUMERIC)
195	cbauer	1.1	// may have to be changed to ((x)>=0x80000000U)
196	frink	1.26
197			// has been changed
198			//#define is_a_numeric_hash(x) ((x)&0x80000000U)
199	cbauer	1.1
200			// global functions
201
202	kreckel	1.20	const numeric exp(const numeric & x);
203			const numeric log(const numeric & x);
204			const numeric sin(const numeric & x);
205			const numeric cos(const numeric & x);
206			const numeric tan(const numeric & x);
207			const numeric asin(const numeric & x);
208			const numeric acos(const numeric & x);
209			const numeric atan(const numeric & x);
210			const numeric atan(const numeric & y, const numeric & x);
211			const numeric sinh(const numeric & x);
212			const numeric cosh(const numeric & x);
213			const numeric tanh(const numeric & x);
214			const numeric asinh(const numeric & x);
215			const numeric acosh(const numeric & x);
216			const numeric atanh(const numeric & x);
217	kreckel	1.36	const numeric Li2(const numeric & x);
218	kreckel	1.20	const numeric zeta(const numeric & x);
219	kreckel	1.30	const numeric lgamma(const numeric & x);
220			const numeric tgamma(const numeric & x);
221	kreckel	1.20	const numeric psi(const numeric & x);
222			const numeric psi(const numeric & n, const numeric & x);
223			const numeric factorial(const numeric & n);
224			const numeric doublefactorial(const numeric & n);
225			const numeric binomial(const numeric & n, const numeric & k);
226			const numeric bernoulli(const numeric & n);
227			const numeric fibonacci(const numeric & n);
228	kreckel	1.41	const numeric abs(const numeric & x);
229			const numeric isqrt(const numeric & x);
230			const numeric sqrt(const numeric & x);
231			const numeric abs(const numeric & x);
232			const numeric mod(const numeric & a, const numeric & b);
233			const numeric smod(const numeric & a, const numeric & b);
234			const numeric irem(const numeric & a, const numeric & b);
235			const numeric irem(const numeric & a, const numeric & b, numeric & q);
236			const numeric iquo(const numeric & a, const numeric & b);
237			const numeric iquo(const numeric & a, const numeric & b, numeric & r);
238			const numeric gcd(const numeric & a, const numeric & b);
239			const numeric lcm(const numeric & a, const numeric & b);
240	cbauer	1.1
241			// wrapper functions around member functions
242	kreckel	1.41	inline const numeric pow(const numeric & x, const numeric & y)
243	kreckel	1.16	{ return x.power(y); }
244
245	kreckel	1.41	inline const numeric inverse(const numeric & x)
246	cbauer	1.1	{ return x.inverse(); }
247	kreckel	1.6
248	kreckel	1.32	inline int csgn(const numeric & x)
249	kreckel	1.6	{ return x.csgn(); }
250	cbauer	1.1
251	kreckel	1.16	inline bool is_zero(const numeric & x)
252	cbauer	1.1	{ return x.is_zero(); }
253
254	kreckel	1.16	inline bool is_positive(const numeric & x)
255	cbauer	1.1	{ return x.is_positive(); }
256
257	kreckel	1.16	inline bool is_integer(const numeric & x)
258	cbauer	1.1	{ return x.is_integer(); }
259
260	kreckel	1.16	inline bool is_pos_integer(const numeric & x)
261	cbauer	1.1	{ return x.is_pos_integer(); }
262
263	kreckel	1.16	inline bool is_nonneg_integer(const numeric & x)
264	cbauer	1.1	{ return x.is_nonneg_integer(); }
265
266	kreckel	1.16	inline bool is_even(const numeric & x)
267	cbauer	1.1	{ return x.is_even(); }
268
269	kreckel	1.16	inline bool is_odd(const numeric & x)
270	cbauer	1.1	{ return x.is_odd(); }
271
272	kreckel	1.16	inline bool is_prime(const numeric & x)
273	cbauer	1.1	{ return x.is_prime(); }
274
275	kreckel	1.16	inline bool is_rational(const numeric & x)
276	cbauer	1.1	{ return x.is_rational(); }
277
278	kreckel	1.16	inline bool is_real(const numeric & x)
279	cbauer	1.1	{ return x.is_real(); }
280
281	kreckel	1.16	inline bool is_cinteger(const numeric & x)
282	kreckel	1.14	{ return x.is_cinteger(); }
283
284	kreckel	1.16	inline bool is_crational(const numeric & x)
285	kreckel	1.14	{ return x.is_crational(); }
286	kreckel	1.42
287			inline int to_int(const numeric & x)
288			{ return x.to_int(); }
289
290			inline long to_long(const numeric & x)
291			{ return x.to_long(); }
292
293			inline double to_double(const numeric & x)
294			{ return x.to_double(); }
295	kreckel	1.14
296	kreckel	1.32	inline const numeric real(const numeric & x)
297	cbauer	1.1	{ return x.real(); }
298
299	kreckel	1.32	inline const numeric imag(const numeric & x)
300	cbauer	1.1	{ return x.imag(); }
301
302	kreckel	1.32	inline const numeric numer(const numeric & x)
303	cbauer	1.1	{ return x.numer(); }
304
305	kreckel	1.32	inline const numeric denom(const numeric & x)
306	cbauer	1.1	{ return x.denom(); }
307
308	kreckel	1.11	// numeric evaluation functions for class constant objects:
309
310	cbauer	1.1	ex PiEvalf(void);
311	kreckel	1.31	ex EulerEvalf(void);
312	cbauer	1.1	ex CatalanEvalf(void);
313
314	kreckel	1.23
315	cbauer	1.5	// utility functions
316	kreckel	1.23	inline const numeric &ex_to_numeric(const ex &e)
317			{
318	cbauer	1.38	return static_cast<const numeric &>(*e.bp);
319	kreckel	1.23	}
320
321	cbauer	1.1
322	kreckel	1.22	#ifndef NO_NAMESPACE_GINAC
323	cbauer	1.5	} // namespace GiNaC
324	kreckel	1.22	#endif // ndef NO_NAMESPACE_GINAC
325	kreckel	1.41
326			#ifdef __MAKECINT__
327			#pragma link off defined_in cln/number.h;
328			#pragma link off defined_in cln/complex_class.h;
329			#endif
330	cbauer	1.1
331	cbauer	1.2	#endif // ndef __GINAC_NUMERIC_H__
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