3 * Makes the interface to the underlying bignum package available. */
6 * GiNaC Copyright (C) 1999-2008 Johannes Gutenberg University Mainz, Germany
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.
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.
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., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
23 #ifndef __GINAC_NUMERIC_H__
24 #define __GINAC_NUMERIC_H__
33 #include <cln/complex.h>
35 #if defined(G__CINTVERSION) && !defined(__MAKECINT__)
36 // Cint @$#$! doesn't like forward declaring classes used for casting operators
37 // so we have to include the definition of cln::cl_N here, but it is enough to
38 // do so for the compiler, hence the !defined(__MAKECINT__).
39 #include <cln/complex_class.h>
44 /** Function pointer to implement callbacks in the case 'Digits' gets changed.
45 * Main purpose of such callbacks is to adjust look-up tables of certain
46 * functions to the new precision. Parameter contains the signed difference
47 * between new Digits and old Digits. */
48 typedef void (* digits_changed_callback)(long);
50 /** This class is used to instantiate a global singleton object Digits
51 * which behaves just like Maple's Digits. We need an object rather
52 * than a dumber basic type since as a side-effect we let it change
53 * cl_default_float_format when it gets changed. The only other
54 * meaningful thing to do with it is converting it to an unsigned,
55 * for temprary storing its value e.g. The user must not create an
56 * own working object of this class! Since C++ forces us to make the
57 * class definition visible in order to use an object we put in a
58 * flag which prevents other objects of that class to be created. */
64 _numeric_digits& operator=(long prec);
66 void print(std::ostream& os) const;
67 void add_callback(digits_changed_callback callback);
70 long digits; ///< Number of decimal digits
71 static bool too_late; ///< Already one object present
72 // Holds a list of functions that get called when digits is changed.
73 std::vector<digits_changed_callback> callbacklist;
77 /** Exception class thrown when a singularity is encountered. */
78 class pole_error : public std::domain_error {
80 explicit pole_error(const std::string& what_arg, int degree);
87 /** This class is a wrapper around CLN-numbers within the GiNaC class
88 * hierarchy. Objects of this type may directly be created by the user.*/
89 class numeric : public basic
91 GINAC_DECLARE_REGISTERED_CLASS(numeric, basic)
98 numeric(unsigned int i);
100 numeric(unsigned long i);
101 numeric(long numer, long denom);
103 numeric(const char *);
105 // functions overriding virtual functions from base classes
107 unsigned precedence() const {return 30;}
108 bool info(unsigned inf) const;
109 bool is_polynomial(const ex & var) const;
110 int degree(const ex & s) const;
111 int ldegree(const ex & s) const;
112 ex coeff(const ex & s, int n = 1) const;
113 bool has(const ex &other, unsigned options = 0) const;
114 ex eval(int level = 0) const;
115 ex evalf(int level = 0) const;
116 ex subs(const exmap & m, unsigned options = 0) const { return subs_one_level(m, options); } // overwrites basic::subs() for performance reasons
117 ex normal(exmap & repl, exmap & rev_lookup, int level = 0) const;
118 ex to_rational(exmap & repl) const;
119 ex to_polynomial(exmap & repl) const;
120 numeric integer_content() const;
121 ex smod(const numeric &xi) const;
122 numeric max_coefficient() const;
123 ex conjugate() const;
124 ex real_part() const;
125 ex imag_part() const;
126 /** Save (a.k.a. serialize) object into archive. */
127 void archive(archive_node& n) const;
128 /** Read (a.k.a. deserialize) object from archive. */
129 void read_archive(const archive_node& n, lst& syms);
131 /** Implementation of ex::diff for a numeric always returns 0.
133 ex derivative(const symbol &s) const { return 0; }
134 bool is_equal_same_type(const basic &other) const;
135 unsigned calchash() const;
137 // new virtual functions which can be overridden by derived classes
140 // non-virtual functions in this class
142 const numeric add(const numeric &other) const;
143 const numeric sub(const numeric &other) const;
144 const numeric mul(const numeric &other) const;
145 const numeric div(const numeric &other) const;
146 const numeric power(const numeric &other) const;
147 const numeric & add_dyn(const numeric &other) const;
148 const numeric & sub_dyn(const numeric &other) const;
149 const numeric & mul_dyn(const numeric &other) const;
150 const numeric & div_dyn(const numeric &other) const;
151 const numeric & power_dyn(const numeric &other) const;
152 const numeric & operator=(int i);
153 const numeric & operator=(unsigned int i);
154 const numeric & operator=(long i);
155 const numeric & operator=(unsigned long i);
156 const numeric & operator=(double d);
157 const numeric & operator=(const char *s);
158 const numeric inverse() const;
159 numeric step() const;
161 int compare(const numeric &other) const;
162 bool is_equal(const numeric &other) const;
163 bool is_zero() const;
164 bool is_positive() const;
165 bool is_negative() const;
166 bool is_integer() const;
167 bool is_pos_integer() const;
168 bool is_nonneg_integer() const;
169 bool is_even() const;
171 bool is_prime() const;
172 bool is_rational() const;
173 bool is_real() const;
174 bool is_cinteger() const;
175 bool is_crational() const;
176 bool operator==(const numeric &other) const;
177 bool operator!=(const numeric &other) const;
178 bool operator<(const numeric &other) const;
179 bool operator<=(const numeric &other) const;
180 bool operator>(const numeric &other) const;
181 bool operator>=(const numeric &other) const;
183 long to_long() const;
184 double to_double() const;
185 cln::cl_N to_cl_N() const;
186 const numeric real() const;
187 const numeric imag() const;
188 const numeric numer() const;
189 const numeric denom() const;
190 int int_length() const;
191 // converting routines for interfacing with CLN:
192 explicit numeric(const cln::cl_N &z);
195 void print_numeric(const print_context & c, const char *par_open, const char *par_close, const char *imag_sym, const char *mul_sym, unsigned level) const;
196 void do_print(const print_context & c, unsigned level) const;
197 void do_print_latex(const print_latex & c, unsigned level) const;
198 void do_print_csrc(const print_csrc & c, unsigned level) const;
199 void do_print_csrc_cl_N(const print_csrc_cl_N & c, unsigned level) const;
200 void do_print_tree(const print_tree & c, unsigned level) const;
201 void do_print_python_repr(const print_python_repr & c, unsigned level) const;
208 GINAC_DECLARE_UNARCHIVER(numeric);
213 extern const numeric I;
214 extern _numeric_digits Digits;
218 const numeric exp(const numeric &x);
219 const numeric log(const numeric &x);
220 const numeric sin(const numeric &x);
221 const numeric cos(const numeric &x);
222 const numeric tan(const numeric &x);
223 const numeric asin(const numeric &x);
224 const numeric acos(const numeric &x);
225 const numeric atan(const numeric &x);
226 const numeric atan(const numeric &y, const numeric &x);
227 const numeric sinh(const numeric &x);
228 const numeric cosh(const numeric &x);
229 const numeric tanh(const numeric &x);
230 const numeric asinh(const numeric &x);
231 const numeric acosh(const numeric &x);
232 const numeric atanh(const numeric &x);
233 const numeric Li2(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 const numeric isqrt(const numeric &x);
245 const numeric sqrt(const numeric &x);
246 const numeric abs(const numeric &x);
247 const numeric mod(const numeric &a, const numeric &b);
248 const numeric smod(const numeric &a, const numeric &b);
249 const numeric irem(const numeric &a, const numeric &b);
250 const numeric irem(const numeric &a, const numeric &b, numeric &q);
251 const numeric iquo(const numeric &a, const numeric &b);
252 const numeric iquo(const numeric &a, const numeric &b, numeric &r);
253 const numeric gcd(const numeric &a, const numeric &b);
254 const numeric lcm(const numeric &a, const numeric &b);
256 // wrapper functions around member functions
257 inline const numeric pow(const numeric &x, const numeric &y)
258 { return x.power(y); }
260 inline const numeric inverse(const numeric &x)
261 { return x.inverse(); }
263 inline numeric step(const numeric &x)
266 inline int csgn(const numeric &x)
269 inline bool is_zero(const numeric &x)
270 { return x.is_zero(); }
272 inline bool is_positive(const numeric &x)
273 { return x.is_positive(); }
275 inline bool is_negative(const numeric &x)
276 { return x.is_negative(); }
278 inline bool is_integer(const numeric &x)
279 { return x.is_integer(); }
281 inline bool is_pos_integer(const numeric &x)
282 { return x.is_pos_integer(); }
284 inline bool is_nonneg_integer(const numeric &x)
285 { return x.is_nonneg_integer(); }
287 inline bool is_even(const numeric &x)
288 { return x.is_even(); }
290 inline bool is_odd(const numeric &x)
291 { return x.is_odd(); }
293 inline bool is_prime(const numeric &x)
294 { return x.is_prime(); }
296 inline bool is_rational(const numeric &x)
297 { return x.is_rational(); }
299 inline bool is_real(const numeric &x)
300 { return x.is_real(); }
302 inline bool is_cinteger(const numeric &x)
303 { return x.is_cinteger(); }
305 inline bool is_crational(const numeric &x)
306 { return x.is_crational(); }
308 inline int to_int(const numeric &x)
309 { return x.to_int(); }
311 inline long to_long(const numeric &x)
312 { return x.to_long(); }
314 inline double to_double(const numeric &x)
315 { return x.to_double(); }
317 inline const numeric real(const numeric &x)
320 inline const numeric imag(const numeric &x)
323 inline const numeric numer(const numeric &x)
324 { return x.numer(); }
326 inline const numeric denom(const numeric &x)
327 { return x.denom(); }
329 // numeric evaluation functions for class constant objects:
339 #pragma link off defined_in cln/number.h;
340 #pragma link off defined_in cln/complex_class.h;
343 #endif // ndef __GINAC_NUMERIC_H__