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.

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

// member functions

    // default constructor, destructor, copy constructor assignment
    // operator and helpers
public:
    numeric();
    ~numeric();
    numeric(numeric const & other);
    numeric const & operator=(numeric const & other);
protected:
    void copy(numeric const & 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 printraw(ostream & os) const;
    void printtree(ostream & os, unsigned indent) const;
    void print(ostream & os, unsigned precedence=0) 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(numeric const &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(numeric const & other) const;
    numeric sub(numeric const & other) const;
    numeric mul(numeric const & other) const;
    numeric div(numeric const & other) const;
    numeric power(numeric const & other) const;
    numeric const & add_dyn(numeric const & other) const;
    numeric const & sub_dyn(numeric const & other) const;
    numeric const & mul_dyn(numeric const & other) const;
    numeric const & div_dyn(numeric const & other) const;
    numeric const & power_dyn(numeric const & other) const;
    numeric const & operator=(int i);
    numeric const & operator=(unsigned int i);
    numeric const & operator=(long i);
    numeric const & operator=(unsigned long i);
    numeric const & operator=(double d);
    numeric const & operator=(char const * s);
    /*
    numeric add_dyn(numeric const & other) const   { return add(other);   }
    numeric sub_dyn(numeric const & other) const   { return sub(other);   }
    numeric mul_dyn(numeric const & other) const   { return mul(other);   }
    numeric div_dyn(numeric const & other) const   { return div(other);   }
    numeric power_dyn(numeric const & other) const { return power(other); }
    */
    numeric inverse(void) const;
    int csgn(void) const;
    int compare(numeric const & other) const;
    bool is_equal(numeric const & 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 operator==(numeric const & other) const;
    bool operator!=(numeric const & other) const;
    bool operator<(numeric const & other) const;
    bool operator<=(numeric const & other) const;
    bool operator>(numeric const & other) const;
    bool operator>=(numeric const & 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 const & numZERO(void);
numeric const & numONE(void);
numeric const & numTWO(void);
numeric const & numMINUSONE(void);
numeric const & numHALF(void);

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

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

numeric gcd(numeric const & a, numeric const & b);
numeric lcm(numeric const & a, numeric const & 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 inverse(numeric const & x)
{ return x.inverse(); }

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

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

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

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

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

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

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

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

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

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

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

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

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

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

inline numeric denom(numeric const & 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);
}

} // namespace GiNaC

#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	cbauer	1.5	namespace GiNaC {
34
35			#define HASHVALUE_NUMERIC 0x80000001U
36
37	cbauer	1.1	/** This class is used to instantiate a global object Digits which
38			* behaves just like Maple's Digits. We need an object rather than a
39			* dumber basic type since as a side-effect we let it change
40			* cl_default_float_format when it gets changed. The only other
41			* meaningful thing to do with it is converting it to an unsigned,
42			* for temprary storing its value e.g. The user must not create an
43			* own working object of this class! Since C++ forces us to make the
44			* class definition visible in order to use an object we put in a
45			* flag which prevents other objects of that class to be created. */
46			class _numeric_digits
47			{
48			// member functions
49			public:
50			_numeric_digits();
51			_numeric_digits& operator=(long prec);
52			operator long();
53			void print(ostream & os) const;
54			// member variables
55			private:
56			long digits;
57			static bool too_late;
58			};
59
60			/** This class is a wrapper around CLN-numbers within the GiNaC class
61			* hierarchy. Objects of this type may directly be created by the user.*/
62			class numeric : public basic
63			{
64			// friends
65			friend numeric exp(numeric const & x);
66			friend numeric log(numeric const & x);
67			friend numeric sin(numeric const & x);
68			friend numeric cos(numeric const & x);
69			friend numeric tan(numeric const & x);
70			friend numeric asin(numeric const & x);
71			friend numeric acos(numeric const & x);
72			friend numeric atan(numeric const & x);
73			friend numeric atan(numeric const & y, numeric const & x);
74			friend numeric sinh(numeric const & x);
75			friend numeric cosh(numeric const & x);
76			friend numeric tanh(numeric const & x);
77			friend numeric asinh(numeric const & x);
78			friend numeric acosh(numeric const & x);
79			friend numeric atanh(numeric const & x);
80	kreckel	1.8	friend numeric bernoulli(numeric const & n);
81	cbauer	1.1	friend numeric abs(numeric const & x);
82			friend numeric mod(numeric const & a, numeric const & b);
83			friend numeric smod(numeric const & a, numeric const & b);
84			friend numeric irem(numeric const & a, numeric const & b);
85			friend numeric irem(numeric const & a, numeric const & b, numeric & q);
86			friend numeric iquo(numeric const & a, numeric const & b);
87			friend numeric iquo(numeric const & a, numeric const & b, numeric & r);
88			friend numeric sqrt(numeric const & x);
89			friend numeric isqrt(numeric const & x);
90			friend numeric gcd(numeric const & a, numeric const & b);
91			friend numeric lcm(numeric const & a, numeric const & b);
92			friend numeric const & numZERO(void);
93			friend numeric const & numONE(void);
94			friend numeric const & numTWO(void);
95			friend numeric const & numTHREE(void);
96			friend numeric const & numMINUSONE(void);
97			friend numeric const & numHALF(void);
98
99			// member functions
100
101			// default constructor, destructor, copy constructor assignment
102			// operator and helpers
103			public:
104			numeric();
105			~numeric();
106			numeric(numeric const & other);
107			numeric const & operator=(numeric const & other);
108			protected:
109			void copy(numeric const & 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(char const *);
121			numeric(cl_N const & z);
122
123			// functions overriding virtual functions from bases classes
124			public:
125			basic * duplicate() const;
126			void printraw(ostream & os) const;
127			void printtree(ostream & os, unsigned indent) const;
128			void print(ostream & os, unsigned precedence=0) const;
129			void printcsrc(ostream & os, unsigned type, unsigned precedence=0) const;
130			bool info(unsigned inf) const;
131			ex evalf(int level=0) const;
132			ex diff(symbol const & s) const;
133			ex normal(lst &sym_lst, lst &repl_lst, int level=0) const;
134			numeric integer_content(void) const;
135			ex smod(numeric const &xi) const;
136			numeric max_coefficient(void) const;
137			protected:
138			int compare_same_type(basic const & other) const;
139			bool is_equal_same_type(basic const & other) const;
140			unsigned calchash(void) const {
141			hashvalue=HASHVALUE_NUMERIC;
142			return HASHVALUE_NUMERIC;
143			}
144
145			// new virtual functions which can be overridden by derived classes
146			// (none)
147
148			// non-virtual functions in this class
149			public:
150			numeric add(numeric const & other) const;
151			numeric sub(numeric const & other) const;
152			numeric mul(numeric const & other) const;
153			numeric div(numeric const & other) const;
154			numeric power(numeric const & other) const;
155			numeric const & add_dyn(numeric const & other) const;
156			numeric const & sub_dyn(numeric const & other) const;
157			numeric const & mul_dyn(numeric const & other) const;
158			numeric const & div_dyn(numeric const & other) const;
159			numeric const & power_dyn(numeric const & other) const;
160			numeric const & operator=(int i);
161			numeric const & operator=(unsigned int i);
162			numeric const & operator=(long i);
163			numeric const & operator=(unsigned long i);
164			numeric const & operator=(double d);
165			numeric const & operator=(char const * s);
166			/*
167			numeric add_dyn(numeric const & other) const { return add(other); }
168			numeric sub_dyn(numeric const & other) const { return sub(other); }
169			numeric mul_dyn(numeric const & other) const { return mul(other); }
170			numeric div_dyn(numeric const & other) const { return div(other); }
171			numeric power_dyn(numeric const & other) const { return power(other); }
172			*/
173			numeric inverse(void) const;
174	kreckel	1.6	int csgn(void) const;
175	cbauer	1.1	int compare(numeric const & other) const;
176			bool is_equal(numeric const & other) const;
177			bool is_zero(void) const;
178			bool is_positive(void) const;
179			bool is_negative(void) const;
180			bool is_integer(void) const;
181			bool is_pos_integer(void) const;
182			bool is_nonneg_integer(void) const;
183			bool is_even(void) const;
184			bool is_odd(void) const;
185			bool is_prime(void) const;
186			bool is_rational(void) const;
187			bool is_real(void) const;
188			bool operator==(numeric const & other) const;
189			bool operator!=(numeric const & other) const;
190			bool operator<(numeric const & other) const;
191			bool operator<=(numeric const & other) const;
192			bool operator>(numeric const & other) const;
193			bool operator>=(numeric const & other) const;
194			int to_int(void) const;
195			double to_double(void) const;
196			numeric real(void) const;
197			numeric imag(void) const;
198			numeric numer(void) const;
199			numeric denom(void) const;
200			int int_length(void) const;
201
202			// member variables
203
204			protected:
205			static unsigned precedence;
206			cl_N *value;
207			};
208
209			// global constants
210
211			extern const numeric some_numeric;
212			extern const numeric I;
213			extern type_info const & typeid_numeric;
214			extern _numeric_digits Digits;
215
216			#define is_a_numeric_hash(x) ((x)==HASHVALUE_NUMERIC)
217			// may have to be changed to ((x)>=0x80000000U)
218
219			// global functions
220
221			numeric const & numZERO(void);
222			numeric const & numONE(void);
223			numeric const & numTWO(void);
224			numeric const & numMINUSONE(void);
225			numeric const & numHALF(void);
226
227			numeric exp(numeric const & x);
228			numeric log(numeric const & x);
229			numeric sin(numeric const & x);
230			numeric cos(numeric const & x);
231			numeric tan(numeric const & x);
232			numeric asin(numeric const & x);
233			numeric acos(numeric const & x);
234			numeric atan(numeric const & x);
235			numeric atan(numeric const & y, numeric const & x);
236			numeric sinh(numeric const & x);
237			numeric cosh(numeric const & x);
238			numeric tanh(numeric const & x);
239			numeric asinh(numeric const & x);
240			numeric acosh(numeric const & x);
241			numeric atanh(numeric const & x);
242	kreckel	1.7	numeric zeta(numeric const & x);
243	cbauer	1.1	numeric gamma(numeric const & x);
244	kreckel	1.10	numeric psi(numeric const & x);
245	kreckel	1.7	numeric psi(numeric const & n, numeric const & x);
246	cbauer	1.1	numeric factorial(numeric const & n);
247			numeric doublefactorial(numeric const & n);
248			numeric binomial(numeric const & n, numeric const & k);
249	kreckel	1.8	numeric bernoulli(numeric const & n);
250	cbauer	1.1
251			numeric abs(numeric const & x);
252			numeric mod(numeric const & a, numeric const & b);
253			numeric smod(numeric const & a, numeric const & b);
254			numeric irem(numeric const & a, numeric const & b);
255			numeric irem(numeric const & a, numeric const & b, numeric & q);
256			numeric iquo(numeric const & a, numeric const & b);
257			numeric iquo(numeric const & a, numeric const & b, numeric & r);
258			numeric sqrt(numeric const & x);
259			numeric isqrt(numeric const & x);
260
261			numeric gcd(numeric const & a, numeric const & b);
262			numeric lcm(numeric const & a, numeric const & b);
263
264			/** Exception thrown by numeric members to signal failure */
265			struct numeric_fail
266			{
267			int failval;
268			numeric_fail(int n) { failval = n; }
269			};
270
271			// wrapper functions around member functions
272			inline numeric inverse(numeric const & x)
273			{ return x.inverse(); }
274	kreckel	1.6
275			inline bool csgn(numeric const & x)
276			{ return x.csgn(); }
277	cbauer	1.1
278			inline bool is_zero(numeric const & x)
279			{ return x.is_zero(); }
280
281			inline bool is_positive(numeric const & x)
282			{ return x.is_positive(); }
283
284			inline bool is_integer(numeric const & x)
285			{ return x.is_integer(); }
286
287			inline bool is_pos_integer(numeric const & x)
288			{ return x.is_pos_integer(); }
289
290			inline bool is_nonneg_integer(numeric const & x)
291			{ return x.is_nonneg_integer(); }
292
293			inline bool is_even(numeric const & x)
294			{ return x.is_even(); }
295
296			inline bool is_odd(numeric const & x)
297			{ return x.is_odd(); }
298
299			inline bool is_prime(numeric const & x)
300			{ return x.is_prime(); }
301
302			inline bool is_rational(numeric const & x)
303			{ return x.is_rational(); }
304
305			inline bool is_real(numeric const & x)
306			{ return x.is_real(); }
307
308			inline numeric real(numeric const & x)
309			{ return x.real(); }
310
311			inline numeric imag(numeric const & x)
312			{ return x.imag(); }
313
314			inline numeric numer(numeric const & x)
315			{ return x.numer(); }
316
317			inline numeric denom(numeric const & x)
318			{ return x.denom(); }
319
320	kreckel	1.11	// numeric evaluation functions for class constant objects:
321
322	cbauer	1.1	ex PiEvalf(void);
323			ex EulerGammaEvalf(void);
324			ex CatalanEvalf(void);
325
326	cbauer	1.5	// utility functions
327			inline const numeric &ex_to_numeric(const ex &e)
328			{
329			return static_cast<const numeric &>(*e.bp);
330			}
331	cbauer	1.1
332	cbauer	1.5	} // namespace GiNaC
333	cbauer	1.1
334	cbauer	1.2	#endif // ndef __GINAC_NUMERIC_H__
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