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"

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_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(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
    friend const numeric exp(const numeric & x);
    friend const numeric log(const numeric & x);
    friend const numeric sin(const numeric & x);
    friend const numeric cos(const numeric & x);
    friend const numeric tan(const numeric & x);
    friend const numeric asin(const numeric & x);
    friend const numeric acos(const numeric & x);
    friend const numeric atan(const numeric & x);
    friend const numeric atan(const numeric & y, const numeric & x);
    friend const numeric sinh(const numeric & x);
    friend const numeric cosh(const numeric & x);
    friend const numeric tanh(const numeric & x);
    friend const numeric asinh(const numeric & x);
    friend const numeric acosh(const numeric & x);
    friend const numeric atanh(const numeric & x);
    friend const numeric zeta(const numeric & x);
    friend const numeric bernoulli(const numeric & n);
    friend const numeric fibonacci(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(const char *);
    numeric(const cl_N & 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;
    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;
    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:
    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=(const char * 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;
    long to_long(void) const;
    double to_double(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;

// member variables

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

// global constants

extern const numeric some_numeric;
extern const numeric I;
extern const 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 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);

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 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 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

#endif // ndef __GINAC_NUMERIC_H__
1	/** @file numeric.h
2	*
3	* Makes the interface to the underlying bignum package available. */
4
5	/*
6	* GiNaC Copyright (C) 1999-2000 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
23	#ifndef __GINAC_NUMERIC_H__
24	#define __GINAC_NUMERIC_H__
25
26	#include <strstream>
27	#include "basic.h"
28	#include "ex.h"
29
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	#ifndef NO_NAMESPACE_GINAC
34	namespace GiNaC {
35	#endif // ndef NO_NAMESPACE_GINAC
36
37	#define HASHVALUE_NUMERIC 0x80000001U
38
39	/** 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	GINAC_DECLARE_REGISTERED_CLASS(numeric, basic)
67
68	// friends
69	friend const numeric exp(const numeric & x);
70	friend const numeric log(const numeric & x);
71	friend const numeric sin(const numeric & x);
72	friend const numeric cos(const numeric & x);
73	friend const numeric tan(const numeric & x);
74	friend const numeric asin(const numeric & x);
75	friend const numeric acos(const numeric & x);
76	friend const numeric atan(const numeric & x);
77	friend const numeric atan(const numeric & y, const numeric & x);
78	friend const numeric sinh(const numeric & x);
79	friend const numeric cosh(const numeric & x);
80	friend const numeric tanh(const numeric & x);
81	friend const numeric asinh(const numeric & x);
82	friend const numeric acosh(const numeric & x);
83	friend const numeric atanh(const numeric & x);
84	friend const numeric zeta(const numeric & x);
85	friend const numeric bernoulli(const numeric & n);
86	friend const numeric fibonacci(const numeric & n);
87	friend numeric abs(const numeric & x);
88	friend numeric mod(const numeric & a, const numeric & b);
89	friend numeric smod(const numeric & a, const numeric & b);
90	friend numeric irem(const numeric & a, const numeric & b);
91	friend numeric irem(const numeric & a, const numeric & b, numeric & q);
92	friend numeric iquo(const numeric & a, const numeric & b);
93	friend numeric iquo(const numeric & a, const numeric & b, numeric & r);
94	friend numeric sqrt(const numeric & x);
95	friend numeric isqrt(const numeric & x);
96	friend numeric gcd(const numeric & a, const numeric & b);
97	friend numeric lcm(const numeric & a, const numeric & b);
98
99	// member functions
100
101	// default constructor, destructor, copy constructor assignment
102	// operator and helpers
103	public:
104	numeric();
105	~numeric();
106	numeric(const numeric & other);
107	const numeric & operator=(const numeric & other);
108	protected:
109	void copy(const numeric & other);
110	void destroy(bool call_parent);
111
112	// other constructors
113	public:
114	explicit numeric(int i);
115	explicit numeric(unsigned int i);
116	explicit numeric(long i);
117	explicit numeric(unsigned long i);
118	explicit numeric(long numer, long denom);
119	explicit numeric(double d);
120	explicit numeric(const char *);
121	numeric(const cl_N & z);
122
123	// functions overriding virtual functions from bases classes
124	public:
125	basic * duplicate() const;
126	void print(ostream & os, unsigned precedence=0) const;
127	void printraw(ostream & os) const;
128	void printtree(ostream & os, unsigned indent) const;
129	void printcsrc(ostream & os, unsigned type, unsigned precedence=0) const;
130	bool info(unsigned inf) const;
131	bool has(const ex & other) const;
132	ex eval(int level=0) const;
133	ex evalf(int level=0) const;
134	ex normal(lst &sym_lst, lst &repl_lst, int level=0) const;
135	numeric integer_content(void) const;
136	ex smod(const numeric &xi) const;
137	numeric max_coefficient(void) const;
138	protected:
139	ex derivative(const symbol & s) const;
140	int compare_same_type(const basic & other) const;
141	bool is_equal_same_type(const basic & other) const;
142	unsigned calchash(void) const;
143
144	// new virtual functions which can be overridden by derived classes
145	// (none)
146
147	// non-virtual functions in this class
148	public:
149	numeric add(const numeric & other) const;
150	numeric sub(const numeric & other) const;
151	numeric mul(const numeric & other) const;
152	numeric div(const numeric & other) const;
153	numeric power(const numeric & other) const;
154	const numeric & add_dyn(const numeric & other) const;
155	const numeric & sub_dyn(const numeric & other) const;
156	const numeric & mul_dyn(const numeric & other) const;
157	const numeric & div_dyn(const numeric & other) const;
158	const numeric & power_dyn(const numeric & other) const;
159	const numeric & operator=(int i);
160	const numeric & operator=(unsigned int i);
161	const numeric & operator=(long i);
162	const numeric & operator=(unsigned long i);
163	const numeric & operator=(double d);
164	const numeric & operator=(const char * s);
165	numeric inverse(void) const;
166	int csgn(void) const;
167	int compare(const numeric & other) const;
168	bool is_equal(const numeric & other) const;
169	bool is_zero(void) const;
170	bool is_positive(void) const;
171	bool is_negative(void) const;
172	bool is_integer(void) const;
173	bool is_pos_integer(void) const;
174	bool is_nonneg_integer(void) const;
175	bool is_even(void) const;
176	bool is_odd(void) const;
177	bool is_prime(void) const;
178	bool is_rational(void) const;
179	bool is_real(void) const;
180	bool is_cinteger(void) const;
181	bool is_crational(void) 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	bool operator>(const numeric & other) const;
187	bool operator>=(const numeric & other) const;
188	int to_int(void) const;
189	long to_long(void) const;
190	double to_double(void) const;
191	const numeric real(void) const;
192	const numeric imag(void) const;
193	const numeric numer(void) const;
194	const numeric denom(void) const;
195	int int_length(void) const;
196
197	// member variables
198
199	protected:
200	static unsigned precedence;
201	cl_N *value;
202	};
203
204	// global constants
205
206	extern const numeric some_numeric;
207	extern const numeric I;
208	extern const type_info & typeid_numeric;
209	extern _numeric_digits Digits;
210
211	//#define is_a_numeric_hash(x) ((x)==HASHVALUE_NUMERIC)
212	// may have to be changed to ((x)>=0x80000000U)
213
214	// has been changed
215	//#define is_a_numeric_hash(x) ((x)&0x80000000U)
216
217	// global functions
218
219	const numeric exp(const numeric & x);
220	const numeric log(const numeric & x);
221	const numeric sin(const numeric & x);
222	const numeric cos(const numeric & x);
223	const numeric tan(const numeric & x);
224	const numeric asin(const numeric & x);
225	const numeric acos(const numeric & x);
226	const numeric atan(const numeric & x);
227	const numeric atan(const numeric & y, const numeric & x);
228	const numeric sinh(const numeric & x);
229	const numeric cosh(const numeric & x);
230	const numeric tanh(const numeric & x);
231	const numeric asinh(const numeric & x);
232	const numeric acosh(const numeric & x);
233	const numeric atanh(const numeric & x);
234	const numeric zeta(const numeric & x);
235	const numeric lgamma(const numeric & x);
236	const numeric tgamma(const numeric & x);
237	const numeric psi(const numeric & x);
238	const numeric psi(const numeric & n, const numeric & x);
239	const numeric factorial(const numeric & n);
240	const numeric doublefactorial(const numeric & n);
241	const numeric binomial(const numeric & n, const numeric & k);
242	const numeric bernoulli(const numeric & n);
243	const numeric fibonacci(const numeric & n);
244
245	numeric abs(const numeric & x);
246	numeric mod(const numeric & a, const numeric & b);
247	numeric smod(const numeric & a, const numeric & b);
248	numeric irem(const numeric & a, const numeric & b);
249	numeric irem(const numeric & a, const numeric & b, numeric & q);
250	numeric iquo(const numeric & a, const numeric & b);
251	numeric iquo(const numeric & a, const numeric & b, numeric & r);
252	numeric sqrt(const numeric & x);
253	numeric isqrt(const numeric & x);
254
255	numeric gcd(const numeric & a, const numeric & b);
256	numeric lcm(const numeric & a, const numeric & b);
257
258	/** Exception thrown by numeric members to signal failure */
259	struct numeric_fail
260	{
261	int failval;
262	numeric_fail(int n) { failval = n; }
263	};
264
265	// wrapper functions around member functions
266	inline numeric pow(const numeric & x, const numeric & y)
267	{ return x.power(y); }
268
269	inline numeric inverse(const numeric & x)
270	{ return x.inverse(); }
271
272	inline int csgn(const numeric & x)
273	{ return x.csgn(); }
274
275	inline bool is_zero(const numeric & x)
276	{ return x.is_zero(); }
277
278	inline bool is_positive(const numeric & x)
279	{ return x.is_positive(); }
280
281	inline bool is_integer(const numeric & x)
282	{ return x.is_integer(); }
283
284	inline bool is_pos_integer(const numeric & x)
285	{ return x.is_pos_integer(); }
286
287	inline bool is_nonneg_integer(const numeric & x)
288	{ return x.is_nonneg_integer(); }
289
290	inline bool is_even(const numeric & x)
291	{ return x.is_even(); }
292
293	inline bool is_odd(const numeric & x)
294	{ return x.is_odd(); }
295
296	inline bool is_prime(const numeric & x)
297	{ return x.is_prime(); }
298
299	inline bool is_rational(const numeric & x)
300	{ return x.is_rational(); }
301
302	inline bool is_real(const numeric & x)
303	{ return x.is_real(); }
304
305	inline bool is_cinteger(const numeric & x)
306	{ return x.is_cinteger(); }
307
308	inline bool is_crational(const numeric & x)
309	{ return x.is_crational(); }
310
311	inline const numeric real(const numeric & x)
312	{ return x.real(); }
313
314	inline const numeric imag(const numeric & x)
315	{ return x.imag(); }
316
317	inline const numeric numer(const numeric & x)
318	{ return x.numer(); }
319
320	inline const numeric denom(const numeric & x)
321	{ return x.denom(); }
322
323	// numeric evaluation functions for class constant objects:
324
325	ex PiEvalf(void);
326	ex EulerEvalf(void);
327	ex CatalanEvalf(void);
328
329
330	// utility functions
331	inline const numeric &ex_to_numeric(const ex &e)
332	{
333	return static_cast<const numeric &>(*e.bp);
334	}
335
336
337	#ifndef NO_NAMESPACE_GINAC
338	} // namespace GiNaC
339	#endif // ndef NO_NAMESPACE_GINAC
340
341	#endif // ndef __GINAC_NUMERIC_H__
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