GiNaC/ginac/numeric.h

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

/*
 *  GiNaC Copyright (C) 1999 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 <ginac/basic.h>
#include <ginac/ex.h>

class cl_N;     // We want to include cln.h only in numeric.cpp in order to 
                // avoid namespace pollution and keep compile-time low.

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

#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(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
{
// friends
    friend numeric exp(const numeric & x);
    friend numeric log(const numeric & x);
    friend numeric sin(const numeric & x);
    friend numeric cos(const numeric & x);
    friend numeric tan(const numeric & x);
    friend numeric asin(const numeric & x);
    friend numeric acos(const numeric & x);
    friend numeric atan(const numeric & x);
    friend numeric atan(const numeric & y, const numeric & x);
    friend numeric sinh(const numeric & x);
    friend numeric cosh(const numeric & x);
    friend numeric tanh(const numeric & x);
    friend numeric asinh(const numeric & x);
    friend numeric acosh(const numeric & x);
    friend numeric atanh(const numeric & x);
    friend numeric zeta(const numeric & x);
    friend numeric bernoulli(const numeric & n);
    friend numeric abs(const numeric & x);
    friend numeric mod(const numeric & a, const numeric & b);
    friend numeric smod(const numeric & a, const numeric & b);
    friend numeric irem(const numeric & a, const numeric & b);
    friend numeric irem(const numeric & a, const numeric & b, numeric & q);
    friend numeric iquo(const numeric & a, const numeric & b);
    friend numeric iquo(const numeric & a, const numeric & b, numeric & r);
    friend numeric sqrt(const numeric & x);
    friend numeric isqrt(const numeric & x);
    friend numeric gcd(const numeric & a, const numeric & b);
    friend numeric lcm(const numeric & a, const numeric & b);

// 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(char const *);
    numeric(cl_N const & z);

    // functions overriding virtual functions from bases classes
public:
    basic * duplicate() const;
    void print(ostream & os, unsigned precedence=0) const;
    void printraw(ostream & os) const;
    void printtree(ostream & os, unsigned indent) const;
    void printcsrc(ostream & os, unsigned type, unsigned precedence=0) const;
    bool info(unsigned inf) const;
    ex evalf(int level=0) const;
    ex diff(symbol const & s) const;
    ex normal(lst &sym_lst, lst &repl_lst, int level=0) const;
    numeric integer_content(void) const;
    ex smod(const numeric &xi) const;
    numeric max_coefficient(void) const;
protected:
    int compare_same_type(basic const & other) const;
    bool is_equal_same_type(basic const & other) const;
    unsigned calchash(void) const {
        hashvalue=HASHVALUE_NUMERIC;
        return HASHVALUE_NUMERIC;
    }

    // new virtual functions which can be overridden by derived classes
    // (none)

    // non-virtual functions in this class
public:
    numeric add(const numeric & other) const;
    numeric sub(const numeric & other) const;
    numeric mul(const numeric & other) const;
    numeric div(const numeric & other) 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=(char const * s);
    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;
    double to_double(void) const;
    numeric real(void) const;
    numeric imag(void) const;
    numeric numer(void) const;
    numeric denom(void) const;
    int int_length(void) const;

// member variables

protected:
    static unsigned precedence;
    cl_N *value;
};

// global constants

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

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

// global functions

numeric exp(const numeric & x);
numeric log(const numeric & x);
numeric sin(const numeric & x);
numeric cos(const numeric & x);
numeric tan(const numeric & x);
numeric asin(const numeric & x);
numeric acos(const numeric & x);
numeric atan(const numeric & x);
numeric atan(const numeric & y, const numeric & x);
numeric sinh(const numeric & x);
numeric cosh(const numeric & x);
numeric tanh(const numeric & x);
numeric asinh(const numeric & x);
numeric acosh(const numeric & x);
numeric atanh(const numeric & x);
numeric zeta(const numeric & x);
numeric gamma(const numeric & x);
numeric psi(const numeric & x);
numeric psi(const numeric & n, const numeric & x);
numeric factorial(const numeric & n);
numeric doublefactorial(const numeric & n);
numeric binomial(const numeric & n, const numeric & k);
numeric bernoulli(const numeric & n);

numeric abs(const numeric & x);
numeric mod(const numeric & a, const numeric & b);
numeric smod(const numeric & a, const numeric & b);
numeric irem(const numeric & a, const numeric & b);
numeric irem(const numeric & a, const numeric & b, numeric & q);
numeric iquo(const numeric & a, const numeric & b);
numeric iquo(const numeric & a, const numeric & b, numeric & r);
numeric sqrt(const numeric & x);
numeric isqrt(const numeric & x);

numeric gcd(const numeric & a, const numeric & b);
numeric lcm(const numeric & a, const numeric & b);

/** Exception thrown by numeric members to signal failure */
struct numeric_fail
{
    int failval;
    numeric_fail(int n) { failval = n; }
};

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

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

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

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

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

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

// numeric evaluation functions for class constant objects:

ex PiEvalf(void);
ex EulerGammaEvalf(void);
ex CatalanEvalf(void);

// utility functions
inline const numeric &ex_to_numeric(const ex &e)
{
    return static_cast<const numeric &>(*e.bp);
}

#ifndef NO_GINAC_NAMESPACE
} // namespace GiNaC
#endif // ndef NO_GINAC_NAMESPACE

#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	cbauer	1.2	* GiNaC Copyright (C) 1999 Johannes Gutenberg University Mainz, Germany
7			*
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	1.3	#include <ginac/basic.h>
28	cbauer	1.5	#include <ginac/ex.h>
29	cbauer	1.1
30			class cl_N; // We want to include cln.h only in numeric.cpp in order to
31			// avoid namespace pollution and keep compile-time low.
32
33	frink	1.12	#ifndef NO_GINAC_NAMESPACE
34	cbauer	1.5	namespace GiNaC {
35	frink	1.12	#endif // ndef NO_GINAC_NAMESPACE
36	cbauer	1.5
37			#define HASHVALUE_NUMERIC 0x80000001U
38
39	cbauer	1.1	/** This class is used to instantiate a global object Digits which
40			* behaves just like Maple's Digits. We need an object rather than a
41			* dumber basic type since as a side-effect we let it change
42			* cl_default_float_format when it gets changed. The only other
43			* meaningful thing to do with it is converting it to an unsigned,
44			* for temprary storing its value e.g. The user must not create an
45			* own working object of this class! Since C++ forces us to make the
46			* class definition visible in order to use an object we put in a
47			* flag which prevents other objects of that class to be created. */
48			class _numeric_digits
49			{
50			// member functions
51			public:
52			_numeric_digits();
53			_numeric_digits& operator=(long prec);
54			operator long();
55			void print(ostream & os) const;
56			// member variables
57			private:
58			long digits;
59			static bool too_late;
60			};
61
62			/** This class is a wrapper around CLN-numbers within the GiNaC class
63			* hierarchy. Objects of this type may directly be created by the user.*/
64			class numeric : public basic
65			{
66			// friends
67	kreckel	1.16	friend numeric exp(const numeric & x);
68			friend numeric log(const numeric & x);
69			friend numeric sin(const numeric & x);
70			friend numeric cos(const numeric & x);
71			friend numeric tan(const numeric & x);
72			friend numeric asin(const numeric & x);
73			friend numeric acos(const numeric & x);
74			friend numeric atan(const numeric & x);
75			friend numeric atan(const numeric & y, const numeric & x);
76			friend numeric sinh(const numeric & x);
77			friend numeric cosh(const numeric & x);
78			friend numeric tanh(const numeric & x);
79			friend numeric asinh(const numeric & x);
80			friend numeric acosh(const numeric & x);
81			friend numeric atanh(const numeric & x);
82			friend numeric zeta(const numeric & x);
83			friend numeric bernoulli(const numeric & n);
84			friend numeric abs(const numeric & x);
85			friend numeric mod(const numeric & a, const numeric & b);
86			friend numeric smod(const numeric & a, const numeric & b);
87			friend numeric irem(const numeric & a, const numeric & b);
88			friend numeric irem(const numeric & a, const numeric & b, numeric & q);
89			friend numeric iquo(const numeric & a, const numeric & b);
90			friend numeric iquo(const numeric & a, const numeric & b, numeric & r);
91			friend numeric sqrt(const numeric & x);
92			friend numeric isqrt(const numeric & x);
93			friend numeric gcd(const numeric & a, const numeric & b);
94			friend numeric lcm(const numeric & a, const numeric & b);
95	cbauer	1.1
96			// member functions
97
98			// default constructor, destructor, copy constructor assignment
99			// operator and helpers
100			public:
101			numeric();
102			~numeric();
103	kreckel	1.16	numeric(const numeric & other);
104			const numeric & operator=(const numeric & other);
105	cbauer	1.1	protected:
106	kreckel	1.16	void copy(const numeric & other);
107	cbauer	1.1	void destroy(bool call_parent);
108
109			// other constructors
110			public:
111			explicit numeric(int i);
112			explicit numeric(unsigned int i);
113			explicit numeric(long i);
114			explicit numeric(unsigned long i);
115			explicit numeric(long numer, long denom);
116			explicit numeric(double d);
117			explicit numeric(char const *);
118			numeric(cl_N const & z);
119
120			// functions overriding virtual functions from bases classes
121			public:
122			basic * duplicate() const;
123	kreckel	1.14	void print(ostream & os, unsigned precedence=0) const;
124	cbauer	1.1	void printraw(ostream & os) const;
125			void printtree(ostream & os, unsigned indent) const;
126			void printcsrc(ostream & os, unsigned type, unsigned precedence=0) const;
127			bool info(unsigned inf) const;
128			ex evalf(int level=0) const;
129			ex diff(symbol const & s) const;
130			ex normal(lst &sym_lst, lst &repl_lst, int level=0) const;
131			numeric integer_content(void) const;
132	kreckel	1.16	ex smod(const numeric &xi) const;
133	cbauer	1.1	numeric max_coefficient(void) const;
134			protected:
135			int compare_same_type(basic const & other) const;
136			bool is_equal_same_type(basic const & other) const;
137			unsigned calchash(void) const {
138			hashvalue=HASHVALUE_NUMERIC;
139			return HASHVALUE_NUMERIC;
140			}
141
142			// new virtual functions which can be overridden by derived classes
143			// (none)
144
145			// non-virtual functions in this class
146			public:
147	kreckel	1.16	numeric add(const numeric & other) const;
148			numeric sub(const numeric & other) const;
149			numeric mul(const numeric & other) const;
150			numeric div(const numeric & other) const;
151			numeric power(const numeric & other) const;
152			const numeric & add_dyn(const numeric & other) const;
153			const numeric & sub_dyn(const numeric & other) const;
154			const numeric & mul_dyn(const numeric & other) const;
155			const numeric & div_dyn(const numeric & other) const;
156			const numeric & power_dyn(const numeric & other) const;
157			const numeric & operator=(int i);
158			const numeric & operator=(unsigned int i);
159			const numeric & operator=(long i);
160			const numeric & operator=(unsigned long i);
161			const numeric & operator=(double d);
162			const numeric & operator=(char const * s);
163	cbauer	1.1	numeric inverse(void) const;
164	kreckel	1.6	int csgn(void) const;
165	kreckel	1.16	int compare(const numeric & other) const;
166			bool is_equal(const numeric & other) const;
167	cbauer	1.1	bool is_zero(void) const;
168			bool is_positive(void) const;
169			bool is_negative(void) const;
170			bool is_integer(void) const;
171			bool is_pos_integer(void) const;
172			bool is_nonneg_integer(void) const;
173			bool is_even(void) const;
174			bool is_odd(void) const;
175			bool is_prime(void) const;
176			bool is_rational(void) const;
177			bool is_real(void) const;
178	kreckel	1.13	bool is_cinteger(void) const;
179			bool is_crational(void) const;
180	kreckel	1.16	bool operator==(const numeric & other) const;
181			bool operator!=(const numeric & other) const;
182			bool operator<(const numeric & other) const;
183			bool operator<=(const numeric & other) const;
184			bool operator>(const numeric & other) const;
185			bool operator>=(const numeric & other) const;
186	cbauer	1.1	int to_int(void) const;
187			double to_double(void) const;
188			numeric real(void) const;
189			numeric imag(void) const;
190			numeric numer(void) const;
191			numeric denom(void) const;
192			int int_length(void) const;
193
194			// member variables
195
196			protected:
197			static unsigned precedence;
198			cl_N *value;
199			};
200
201			// global constants
202
203			extern const numeric some_numeric;
204			extern const numeric I;
205			extern type_info const & typeid_numeric;
206			extern _numeric_digits Digits;
207
208			#define is_a_numeric_hash(x) ((x)==HASHVALUE_NUMERIC)
209			// may have to be changed to ((x)>=0x80000000U)
210
211			// global functions
212
213	kreckel	1.16	numeric exp(const numeric & x);
214			numeric log(const numeric & x);
215			numeric sin(const numeric & x);
216			numeric cos(const numeric & x);
217			numeric tan(const numeric & x);
218			numeric asin(const numeric & x);
219			numeric acos(const numeric & x);
220			numeric atan(const numeric & x);
221			numeric atan(const numeric & y, const numeric & x);
222			numeric sinh(const numeric & x);
223			numeric cosh(const numeric & x);
224			numeric tanh(const numeric & x);
225			numeric asinh(const numeric & x);
226			numeric acosh(const numeric & x);
227			numeric atanh(const numeric & x);
228			numeric zeta(const numeric & x);
229			numeric gamma(const numeric & x);
230			numeric psi(const numeric & x);
231			numeric psi(const numeric & n, const numeric & x);
232			numeric factorial(const numeric & n);
233			numeric doublefactorial(const numeric & n);
234			numeric binomial(const numeric & n, const numeric & k);
235			numeric bernoulli(const numeric & n);
236
237			numeric abs(const numeric & x);
238			numeric mod(const numeric & a, const numeric & b);
239			numeric smod(const numeric & a, const numeric & b);
240			numeric irem(const numeric & a, const numeric & b);
241			numeric irem(const numeric & a, const numeric & b, numeric & q);
242			numeric iquo(const numeric & a, const numeric & b);
243			numeric iquo(const numeric & a, const numeric & b, numeric & r);
244			numeric sqrt(const numeric & x);
245			numeric isqrt(const numeric & x);
246	cbauer	1.1
247	kreckel	1.16	numeric gcd(const numeric & a, const numeric & b);
248			numeric lcm(const numeric & a, const numeric & b);
249	cbauer	1.1
250			/** Exception thrown by numeric members to signal failure */
251			struct numeric_fail
252			{
253			int failval;
254			numeric_fail(int n) { failval = n; }
255			};
256
257			// wrapper functions around member functions
258	kreckel	1.16	inline numeric pow(const numeric & x, const numeric & y)
259			{ return x.power(y); }
260
261			inline numeric inverse(const numeric & x)
262	cbauer	1.1	{ return x.inverse(); }
263	kreckel	1.6
264	kreckel	1.16	inline bool csgn(const numeric & x)
265	kreckel	1.6	{ return x.csgn(); }
266	cbauer	1.1
267	kreckel	1.16	inline bool is_zero(const numeric & x)
268	cbauer	1.1	{ return x.is_zero(); }
269
270	kreckel	1.16	inline bool is_positive(const numeric & x)
271	cbauer	1.1	{ return x.is_positive(); }
272
273	kreckel	1.16	inline bool is_integer(const numeric & x)
274	cbauer	1.1	{ return x.is_integer(); }
275
276	kreckel	1.16	inline bool is_pos_integer(const numeric & x)
277	cbauer	1.1	{ return x.is_pos_integer(); }
278
279	kreckel	1.16	inline bool is_nonneg_integer(const numeric & x)
280	cbauer	1.1	{ return x.is_nonneg_integer(); }
281
282	kreckel	1.16	inline bool is_even(const numeric & x)
283	cbauer	1.1	{ return x.is_even(); }
284
285	kreckel	1.16	inline bool is_odd(const numeric & x)
286	cbauer	1.1	{ return x.is_odd(); }
287
288	kreckel	1.16	inline bool is_prime(const numeric & x)
289	cbauer	1.1	{ return x.is_prime(); }
290
291	kreckel	1.16	inline bool is_rational(const numeric & x)
292	cbauer	1.1	{ return x.is_rational(); }
293
294	kreckel	1.16	inline bool is_real(const numeric & x)
295	cbauer	1.1	{ return x.is_real(); }
296
297	kreckel	1.16	inline bool is_cinteger(const numeric & x)
298	kreckel	1.14	{ return x.is_cinteger(); }
299
300	kreckel	1.16	inline bool is_crational(const numeric & x)
301	kreckel	1.14	{ return x.is_crational(); }
302
303	kreckel	1.16	inline numeric real(const numeric & x)
304	cbauer	1.1	{ return x.real(); }
305
306	kreckel	1.16	inline numeric imag(const numeric & x)
307	cbauer	1.1	{ return x.imag(); }
308
309	kreckel	1.16	inline numeric numer(const numeric & x)
310	cbauer	1.1	{ return x.numer(); }
311
312	kreckel	1.16	inline numeric denom(const numeric & x)
313	cbauer	1.1	{ return x.denom(); }
314
315	kreckel	1.11	// numeric evaluation functions for class constant objects:
316
317	cbauer	1.1	ex PiEvalf(void);
318			ex EulerGammaEvalf(void);
319			ex CatalanEvalf(void);
320
321	cbauer	1.5	// utility functions
322			inline const numeric &ex_to_numeric(const ex &e)
323			{
324	kreckel	1.14	return static_cast<const numeric &>(*e.bp);
325	cbauer	1.5	}
326	cbauer	1.1
327	frink	1.12	#ifndef NO_GINAC_NAMESPACE
328	cbauer	1.5	} // namespace GiNaC
329	frink	1.12	#endif // ndef NO_GINAC_NAMESPACE
330	cbauer	1.1
331	cbauer	1.2	#endif // ndef __GINAC_NUMERIC_H__
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