| 1 |
/** @file numeric.h
|
| 2 |
*
|
| 3 |
* Makes the interface to the underlying bignum package available. */
|
| 4 |
|
| 5 |
/*
|
| 6 |
* 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 |
|
| 23 |
#ifndef __GINAC_NUMERIC_H__
|
| 24 |
#define __GINAC_NUMERIC_H__
|
| 25 |
|
| 26 |
#include <strstream>
|
| 27 |
#include <ginac/basic.h>
|
| 28 |
#include <ginac/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_GINAC_NAMESPACE
|
| 34 |
namespace GiNaC {
|
| 35 |
#endif // ndef NO_GINAC_NAMESPACE
|
| 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 |
// friends
|
| 67 |
friend numeric exp(numeric const & x);
|
| 68 |
friend numeric log(numeric const & x);
|
| 69 |
friend numeric sin(numeric const & x);
|
| 70 |
friend numeric cos(numeric const & x);
|
| 71 |
friend numeric tan(numeric const & x);
|
| 72 |
friend numeric asin(numeric const & x);
|
| 73 |
friend numeric acos(numeric const & x);
|
| 74 |
friend numeric atan(numeric const & x);
|
| 75 |
friend numeric atan(numeric const & y, numeric const & x);
|
| 76 |
friend numeric sinh(numeric const & x);
|
| 77 |
friend numeric cosh(numeric const & x);
|
| 78 |
friend numeric tanh(numeric const & x);
|
| 79 |
friend numeric asinh(numeric const & x);
|
| 80 |
friend numeric acosh(numeric const & x);
|
| 81 |
friend numeric atanh(numeric const & x);
|
| 82 |
friend numeric bernoulli(numeric const & n);
|
| 83 |
friend numeric abs(numeric const & x);
|
| 84 |
friend numeric mod(numeric const & a, numeric const & b);
|
| 85 |
friend numeric smod(numeric const & a, numeric const & b);
|
| 86 |
friend numeric irem(numeric const & a, numeric const & b);
|
| 87 |
friend numeric irem(numeric const & a, numeric const & b, numeric & q);
|
| 88 |
friend numeric iquo(numeric const & a, numeric const & b);
|
| 89 |
friend numeric iquo(numeric const & a, numeric const & b, numeric & r);
|
| 90 |
friend numeric sqrt(numeric const & x);
|
| 91 |
friend numeric isqrt(numeric const & x);
|
| 92 |
friend numeric gcd(numeric const & a, numeric const & b);
|
| 93 |
friend numeric lcm(numeric const & a, numeric const & b);
|
| 94 |
friend numeric const & numZERO(void);
|
| 95 |
friend numeric const & numONE(void);
|
| 96 |
friend numeric const & numTWO(void);
|
| 97 |
friend numeric const & numTHREE(void);
|
| 98 |
friend numeric const & numMINUSONE(void);
|
| 99 |
friend numeric const & numHALF(void);
|
| 100 |
|
| 101 |
// member functions
|
| 102 |
|
| 103 |
// default constructor, destructor, copy constructor assignment
|
| 104 |
// operator and helpers
|
| 105 |
public:
|
| 106 |
numeric();
|
| 107 |
~numeric();
|
| 108 |
numeric(numeric const & other);
|
| 109 |
numeric const & operator=(numeric const & other);
|
| 110 |
protected:
|
| 111 |
void copy(numeric const & other);
|
| 112 |
void destroy(bool call_parent);
|
| 113 |
|
| 114 |
// other constructors
|
| 115 |
public:
|
| 116 |
explicit numeric(int i);
|
| 117 |
explicit numeric(unsigned int i);
|
| 118 |
explicit numeric(long i);
|
| 119 |
explicit numeric(unsigned long i);
|
| 120 |
explicit numeric(long numer, long denom);
|
| 121 |
explicit numeric(double d);
|
| 122 |
explicit numeric(char const *);
|
| 123 |
numeric(cl_N const & z);
|
| 124 |
|
| 125 |
// functions overriding virtual functions from bases classes
|
| 126 |
public:
|
| 127 |
basic * duplicate() const;
|
| 128 |
void printraw(ostream & os) const;
|
| 129 |
void printtree(ostream & os, unsigned indent) const;
|
| 130 |
void print(ostream & os, unsigned precedence=0) const;
|
| 131 |
void printcsrc(ostream & os, unsigned type, unsigned precedence=0) const;
|
| 132 |
bool info(unsigned inf) const;
|
| 133 |
ex evalf(int level=0) const;
|
| 134 |
ex diff(symbol const & s) const;
|
| 135 |
ex normal(lst &sym_lst, lst &repl_lst, int level=0) const;
|
| 136 |
numeric integer_content(void) const;
|
| 137 |
ex smod(numeric const &xi) const;
|
| 138 |
numeric max_coefficient(void) const;
|
| 139 |
protected:
|
| 140 |
int compare_same_type(basic const & other) const;
|
| 141 |
bool is_equal_same_type(basic const & other) const;
|
| 142 |
unsigned calchash(void) const {
|
| 143 |
hashvalue=HASHVALUE_NUMERIC;
|
| 144 |
return HASHVALUE_NUMERIC;
|
| 145 |
}
|
| 146 |
|
| 147 |
// new virtual functions which can be overridden by derived classes
|
| 148 |
// (none)
|
| 149 |
|
| 150 |
// non-virtual functions in this class
|
| 151 |
public:
|
| 152 |
numeric add(numeric const & other) const;
|
| 153 |
numeric sub(numeric const & other) const;
|
| 154 |
numeric mul(numeric const & other) const;
|
| 155 |
numeric div(numeric const & other) const;
|
| 156 |
numeric power(numeric const & other) const;
|
| 157 |
numeric const & add_dyn(numeric const & other) const;
|
| 158 |
numeric const & sub_dyn(numeric const & other) const;
|
| 159 |
numeric const & mul_dyn(numeric const & other) const;
|
| 160 |
numeric const & div_dyn(numeric const & other) const;
|
| 161 |
numeric const & power_dyn(numeric const & other) const;
|
| 162 |
numeric const & operator=(int i);
|
| 163 |
numeric const & operator=(unsigned int i);
|
| 164 |
numeric const & operator=(long i);
|
| 165 |
numeric const & operator=(unsigned long i);
|
| 166 |
numeric const & operator=(double d);
|
| 167 |
numeric const & operator=(char const * s);
|
| 168 |
/*
|
| 169 |
numeric add_dyn(numeric const & other) const { return add(other); }
|
| 170 |
numeric sub_dyn(numeric const & other) const { return sub(other); }
|
| 171 |
numeric mul_dyn(numeric const & other) const { return mul(other); }
|
| 172 |
numeric div_dyn(numeric const & other) const { return div(other); }
|
| 173 |
numeric power_dyn(numeric const & other) const { return power(other); }
|
| 174 |
*/
|
| 175 |
numeric inverse(void) const;
|
| 176 |
int csgn(void) const;
|
| 177 |
int compare(numeric const & other) const;
|
| 178 |
bool is_equal(numeric const & other) const;
|
| 179 |
bool is_zero(void) const;
|
| 180 |
bool is_positive(void) const;
|
| 181 |
bool is_negative(void) const;
|
| 182 |
bool is_integer(void) const;
|
| 183 |
bool is_pos_integer(void) const;
|
| 184 |
bool is_nonneg_integer(void) const;
|
| 185 |
bool is_even(void) const;
|
| 186 |
bool is_odd(void) const;
|
| 187 |
bool is_prime(void) const;
|
| 188 |
bool is_rational(void) const;
|
| 189 |
bool is_real(void) const;
|
| 190 |
bool is_cinteger(void) const;
|
| 191 |
bool is_crational(void) const;
|
| 192 |
bool operator==(numeric const & other) const;
|
| 193 |
bool operator!=(numeric const & other) const;
|
| 194 |
bool operator<(numeric const & other) const;
|
| 195 |
bool operator<=(numeric const & other) const;
|
| 196 |
bool operator>(numeric const & other) const;
|
| 197 |
bool operator>=(numeric const & other) const;
|
| 198 |
int to_int(void) const;
|
| 199 |
double to_double(void) const;
|
| 200 |
numeric real(void) const;
|
| 201 |
numeric imag(void) const;
|
| 202 |
numeric numer(void) const;
|
| 203 |
numeric denom(void) const;
|
| 204 |
int int_length(void) const;
|
| 205 |
|
| 206 |
// member variables
|
| 207 |
|
| 208 |
protected:
|
| 209 |
static unsigned precedence;
|
| 210 |
cl_N *value;
|
| 211 |
};
|
| 212 |
|
| 213 |
// global constants
|
| 214 |
|
| 215 |
extern const numeric some_numeric;
|
| 216 |
extern const numeric I;
|
| 217 |
extern type_info const & typeid_numeric;
|
| 218 |
extern _numeric_digits Digits;
|
| 219 |
|
| 220 |
#define is_a_numeric_hash(x) ((x)==HASHVALUE_NUMERIC)
|
| 221 |
// may have to be changed to ((x)>=0x80000000U)
|
| 222 |
|
| 223 |
// global functions
|
| 224 |
|
| 225 |
numeric const & numZERO(void);
|
| 226 |
numeric const & numONE(void);
|
| 227 |
numeric const & numTWO(void);
|
| 228 |
numeric const & numMINUSONE(void);
|
| 229 |
numeric const & numHALF(void);
|
| 230 |
|
| 231 |
numeric exp(numeric const & x);
|
| 232 |
numeric log(numeric const & x);
|
| 233 |
numeric sin(numeric const & x);
|
| 234 |
numeric cos(numeric const & x);
|
| 235 |
numeric tan(numeric const & x);
|
| 236 |
numeric asin(numeric const & x);
|
| 237 |
numeric acos(numeric const & x);
|
| 238 |
numeric atan(numeric const & x);
|
| 239 |
numeric atan(numeric const & y, numeric const & x);
|
| 240 |
numeric sinh(numeric const & x);
|
| 241 |
numeric cosh(numeric const & x);
|
| 242 |
numeric tanh(numeric const & x);
|
| 243 |
numeric asinh(numeric const & x);
|
| 244 |
numeric acosh(numeric const & x);
|
| 245 |
numeric atanh(numeric const & x);
|
| 246 |
numeric zeta(numeric const & x);
|
| 247 |
numeric gamma(numeric const & x);
|
| 248 |
numeric psi(numeric const & x);
|
| 249 |
numeric psi(numeric const & n, numeric const & x);
|
| 250 |
numeric factorial(numeric const & n);
|
| 251 |
numeric doublefactorial(numeric const & n);
|
| 252 |
numeric binomial(numeric const & n, numeric const & k);
|
| 253 |
numeric bernoulli(numeric const & n);
|
| 254 |
|
| 255 |
numeric abs(numeric const & x);
|
| 256 |
numeric mod(numeric const & a, numeric const & b);
|
| 257 |
numeric smod(numeric const & a, numeric const & b);
|
| 258 |
numeric irem(numeric const & a, numeric const & b);
|
| 259 |
numeric irem(numeric const & a, numeric const & b, numeric & q);
|
| 260 |
numeric iquo(numeric const & a, numeric const & b);
|
| 261 |
numeric iquo(numeric const & a, numeric const & b, numeric & r);
|
| 262 |
numeric sqrt(numeric const & x);
|
| 263 |
numeric isqrt(numeric const & x);
|
| 264 |
|
| 265 |
numeric gcd(numeric const & a, numeric const & b);
|
| 266 |
numeric lcm(numeric const & a, numeric const & b);
|
| 267 |
|
| 268 |
/** Exception thrown by numeric members to signal failure */
|
| 269 |
struct numeric_fail
|
| 270 |
{
|
| 271 |
int failval;
|
| 272 |
numeric_fail(int n) { failval = n; }
|
| 273 |
};
|
| 274 |
|
| 275 |
// wrapper functions around member functions
|
| 276 |
inline numeric inverse(numeric const & x)
|
| 277 |
{ return x.inverse(); }
|
| 278 |
|
| 279 |
inline bool csgn(numeric const & x)
|
| 280 |
{ return x.csgn(); }
|
| 281 |
|
| 282 |
inline bool is_zero(numeric const & x)
|
| 283 |
{ return x.is_zero(); }
|
| 284 |
|
| 285 |
inline bool is_positive(numeric const & x)
|
| 286 |
{ return x.is_positive(); }
|
| 287 |
|
| 288 |
inline bool is_integer(numeric const & x)
|
| 289 |
{ return x.is_integer(); }
|
| 290 |
|
| 291 |
inline bool is_pos_integer(numeric const & x)
|
| 292 |
{ return x.is_pos_integer(); }
|
| 293 |
|
| 294 |
inline bool is_nonneg_integer(numeric const & x)
|
| 295 |
{ return x.is_nonneg_integer(); }
|
| 296 |
|
| 297 |
inline bool is_even(numeric const & x)
|
| 298 |
{ return x.is_even(); }
|
| 299 |
|
| 300 |
inline bool is_odd(numeric const & x)
|
| 301 |
{ return x.is_odd(); }
|
| 302 |
|
| 303 |
inline bool is_prime(numeric const & x)
|
| 304 |
{ return x.is_prime(); }
|
| 305 |
|
| 306 |
inline bool is_rational(numeric const & x)
|
| 307 |
{ return x.is_rational(); }
|
| 308 |
|
| 309 |
inline bool is_real(numeric const & x)
|
| 310 |
{ return x.is_real(); }
|
| 311 |
|
| 312 |
inline numeric real(numeric const & x)
|
| 313 |
{ return x.real(); }
|
| 314 |
|
| 315 |
inline numeric imag(numeric const & x)
|
| 316 |
{ return x.imag(); }
|
| 317 |
|
| 318 |
inline numeric numer(numeric const & x)
|
| 319 |
{ return x.numer(); }
|
| 320 |
|
| 321 |
inline numeric denom(numeric const & x)
|
| 322 |
{ return x.denom(); }
|
| 323 |
|
| 324 |
// numeric evaluation functions for class constant objects:
|
| 325 |
|
| 326 |
ex PiEvalf(void);
|
| 327 |
ex EulerGammaEvalf(void);
|
| 328 |
ex CatalanEvalf(void);
|
| 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 |
#ifndef NO_GINAC_NAMESPACE
|
| 337 |
} // namespace GiNaC
|
| 338 |
#endif // ndef NO_GINAC_NAMESPACE
|
| 339 |
|
| 340 |
#endif // ndef __GINAC_NUMERIC_H__
|
Parent Directory
| 
Revision Log