MADNESS  version 0.9
mpreal.h
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1 /*
2  This file is part of MADNESS.
3 
4  Copyright (C) 2007,2010 Oak Ridge National Laboratory
5 
6  This program is free software; you can redistribute it and/or modify
7  it under the terms of the GNU General Public License as published by
8  the Free Software Foundation; either version 2 of the License, or
9  (at your option) any later version.
10 
11  This program is distributed in the hope that it will be useful,
12  but WITHOUT ANY WARRANTY; without even the implied warranty of
13  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
14  GNU General Public License for more details.
15 
16  You should have received a copy of the GNU General Public License
17  along with this program; if not, write to the Free Software
18  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
19 
20  For more information please contact:
21 
22  Robert J. Harrison
23  Oak Ridge National Laboratory
24  One Bethel Valley Road
25  P.O. Box 2008, MS-6367
26 
27  email: harrisonrj@ornl.gov
28  tel: 865-241-3937
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30 
31  $Id$
32 */
33 /*
34  Multi-precision real number class. C++ wrapper fo MPFR library.
35  Project homepage: http://www.holoborodko.com/pavel/
36  Contact e-mail: pavel@holoborodko.com
37 
38  Copyright (c) 2008 Pavel Holoborodko
39 
40  This library is free software; you can redistribute it and/or
41  modify it under the terms of the GNU Lesser General Public
42  License as published by the Free Software Foundation; either
43  version 2.1 of the License, or (at your option) any later version.
44 
45  This library is distributed in the hope that it will be useful,
46  but WITHOUT ANY WARRANTY; without even the implied warranty of
47  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
48  Lesser General Public License for more details.
49 
50  You should have received a copy of the GNU Lesser General Public
51  License along with this library; if not, write to the Free Software
52  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
53 
54  Contributors:
55  Brain Gladman, Helmut Jarausch, Fokko Beekhof, Ulrich Mutze.
56 */
57 
58 #ifndef __MP_REAL_H__
59 #define __MP_REAL_H__
60 
61 #include <string>
62 #include <iostream>
63 #include <stdexcept>
64 #include <cfloat>
65 #include <cmath>
66 
67 #include "mpfr.h"
68 
69 // Detect compiler using signatures from http://predef.sourceforge.net/
70 // GNU C/C++
71 #if defined(__GNUC__)
72  #define IsInf(x) std::isinf(x) // C99 supported by C++ 2003 standard
73 
74 // Microsoft Visual C++
75 #elif defined(_MSC_VER)
76  #define IsInf(x) (!_finite(x)) // Microsoft specific
77 
78 // Others, will be added as needed
79 #else
80  #define IsInf(x) std::isinf(x) // now just hope for the C99 conformance
81 #endif
82 
83 namespace mpfr {
84 
85 class mpreal {
86 private:
87  mpfr_t mp;
88 
89 public:
90  static mp_rnd_t default_rnd;
91  static mp_prec_t default_prec;
92  static int default_base;
93  static int double_bits;
94 
95 public:
96  // Constructors && type conversion
97  mpreal();
98  mpreal(const mpreal& u);
99 
100  mpreal(const mpfr_t u);
101  mpreal(const mpf_t u);
102 
103  mpreal(const mpz_t u, mp_prec_t prec = default_prec, mp_rnd_t mode = default_rnd);
104  mpreal(const mpq_t u, mp_prec_t prec = default_prec, mp_rnd_t mode = default_rnd);
105  mpreal(const double u, mp_prec_t prec = default_prec, mp_rnd_t mode = default_rnd);
106  mpreal(const long double u, mp_prec_t prec = default_prec, mp_rnd_t mode = default_rnd);
107  mpreal(const unsigned long int u, mp_prec_t prec = default_prec, mp_rnd_t mode = default_rnd);
108  mpreal(const unsigned int u, mp_prec_t prec = default_prec, mp_rnd_t mode = default_rnd);
109  mpreal(const long int u, mp_prec_t prec = default_prec, mp_rnd_t mode = default_rnd);
110  mpreal(const int u, mp_prec_t prec = default_prec, mp_rnd_t mode = default_rnd);
111  mpreal(const char* s, mp_prec_t prec = default_prec, int base = default_base, mp_rnd_t mode = default_rnd);
112 
113  ~mpreal();
114 
115  // Operations
116  // =
117  // +, -, *, /, ++, --, <<, >>
118  // *=, +=, -=, /=,
119  // <, >, ==, <=, >=
120 
121  // =
122  mpreal& operator=(const mpreal& v);
123  mpreal& operator=(const mpf_t v);
124  mpreal& operator=(const mpz_t v);
125  mpreal& operator=(const mpq_t v);
126  mpreal& operator=(const long double v);
127  mpreal& operator=(const double v);
128  mpreal& operator=(const unsigned long int v);
129  mpreal& operator=(const unsigned int v);
130  mpreal& operator=(const long int v);
131  mpreal& operator=(const int v);
132  mpreal& operator=(const char* s);
133 
134  // +
135  mpreal& operator+=(const mpreal& v);
136  mpreal& operator+=(const mpf_t v);
137  mpreal& operator+=(const mpz_t v);
138  mpreal& operator+=(const mpq_t v);
139  mpreal& operator+=(const long double u);
140  mpreal& operator+=(const double u);
141  mpreal& operator+=(const unsigned long int u);
142  mpreal& operator+=(const unsigned int u);
143  mpreal& operator+=(const long int u);
144  mpreal& operator+=(const int u);
145  const mpreal operator+() const;
146  mpreal& operator++ ();
147  const mpreal operator++ (int);
148 
149  // -
150  mpreal& operator-=(const mpreal& v);
151  mpreal& operator-=(const mpz_t v);
152  mpreal& operator-=(const mpq_t v);
153  mpreal& operator-=(const long double u);
154  mpreal& operator-=(const double u);
155  mpreal& operator-=(const unsigned long int u);
156  mpreal& operator-=(const unsigned int u);
157  mpreal& operator-=(const long int u);
158  mpreal& operator-=(const int u);
159  const mpreal operator-() const;
160  friend const mpreal operator-(const unsigned long int b, const mpreal& a);
161  friend const mpreal operator-(const unsigned int b, const mpreal& a);
162  friend const mpreal operator-(const long int b, const mpreal& a);
163  friend const mpreal operator-(const int b, const mpreal& a);
164  friend const mpreal operator-(const double b, const mpreal& a);
165  mpreal& operator-- ();
166  const mpreal operator-- (int);
167 
168  // *
169  mpreal& operator*=(const mpreal& v);
170  mpreal& operator*=(const mpz_t v);
171  mpreal& operator*=(const mpq_t v);
172  mpreal& operator*=(const long double v);
173  mpreal& operator*=(const double v);
174  mpreal& operator*=(const unsigned long int v);
175  mpreal& operator*=(const unsigned int v);
176  mpreal& operator*=(const long int v);
177  mpreal& operator*=(const int v);
178 
179  // /
180  mpreal& operator/=(const mpreal& v);
181  mpreal& operator/=(const mpz_t v);
182  mpreal& operator/=(const mpq_t v);
183  mpreal& operator/=(const long double v);
184  mpreal& operator/=(const double v);
185  mpreal& operator/=(const unsigned long int v);
186  mpreal& operator/=(const unsigned int v);
187  mpreal& operator/=(const long int v);
188  mpreal& operator/=(const int v);
189  friend const mpreal operator/(const unsigned long int b, const mpreal& a);
190  friend const mpreal operator/(const unsigned int b, const mpreal& a);
191  friend const mpreal operator/(const long int b, const mpreal& a);
192  friend const mpreal operator/(const int b, const mpreal& a);
193  friend const mpreal operator/(const double b, const mpreal& a);
194 
195  //<<= Fast Multiplication by 2^u
196  mpreal& operator<<=(const unsigned long int u);
197  mpreal& operator<<=(const unsigned int u);
198  mpreal& operator<<=(const long int u);
199  mpreal& operator<<=(const int u);
200 
201  //>>= Fast Division by 2^u
202  mpreal& operator>>=(const unsigned long int u);
203  mpreal& operator>>=(const unsigned int u);
204  mpreal& operator>>=(const long int u);
205  mpreal& operator>>=(const int u);
206 
207  // Boolean Operators
208  friend bool operator > (const mpreal& a, const mpreal& b);
209  friend bool operator >= (const mpreal& a, const mpreal& b);
210  friend bool operator < (const mpreal& a, const mpreal& b);
211  friend bool operator <= (const mpreal& a, const mpreal& b);
212  friend bool operator == (const mpreal& a, const mpreal& b);
213  friend bool operator != (const mpreal& a, const mpreal& b);
214 
215  // Type Conversion operators
216  operator long double() const;
217  operator double() const;
218  operator float() const;
219  operator unsigned long() const;
220  operator unsigned int() const;
221  operator long() const;
222  operator std::string() const;
223  operator mpfr_ptr();
224 
225  // Math Functions
226  friend const mpreal sqr(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
227  friend const mpreal sqrt(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
228  friend const mpreal sqrt(const unsigned long int v, mp_rnd_t rnd_mode = mpreal::default_rnd);
229  friend const mpreal cbrt(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
230  friend const mpreal root(const mpreal& v, unsigned long int k, mp_rnd_t rnd_mode = mpreal::default_rnd);
231  friend const mpreal pow(const mpreal& a, const mpreal& b, mp_rnd_t rnd_mode = mpreal::default_rnd);
232  friend const mpreal pow(const mpreal& a, const mpz_t b, mp_rnd_t rnd_mode = mpreal::default_rnd);
233  friend const mpreal pow(const mpreal& a, const unsigned long int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
234  friend const mpreal pow(const mpreal& a, const long int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
235  friend const mpreal pow(const unsigned long int a, const mpreal& b, mp_rnd_t rnd_mode = mpreal::default_rnd);
236  friend const mpreal pow(const unsigned long int a, const unsigned long int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
237  friend const mpreal fabs(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
238  friend const mpreal abs(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
239  friend const mpreal dim(const mpreal& a, const mpreal& b, mp_rnd_t rnd_mode = mpreal::default_rnd);
240  friend const mpreal mul_2ui(const mpreal& v, unsigned long int k, mp_rnd_t rnd_mode = mpreal::default_rnd);
241  friend const mpreal mul_2si(const mpreal& v, long int k, mp_rnd_t rnd_mode = mpreal::default_rnd);
242  friend const mpreal div_2ui(const mpreal& v, unsigned long int k, mp_rnd_t rnd_mode = mpreal::default_rnd);
243  friend const mpreal div_2si(const mpreal& v, long int k, mp_rnd_t rnd_mode = mpreal::default_rnd);
244  friend int cmpabs(const mpreal& a,const mpreal& b);
245 
246  friend const mpreal log (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
247  friend const mpreal log2 (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
248  friend const mpreal log10(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
249  friend const mpreal exp (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
250  friend const mpreal exp2 (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
251  friend const mpreal exp10(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
252 
253  friend const mpreal cos(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
254  friend const mpreal sin(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
255  friend const mpreal tan(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
256  friend const mpreal sec(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
257  friend const mpreal csc(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
258  friend const mpreal cot(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
259  friend int sin_cos(mpreal& s, mpreal& c, const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
260 
261  friend const mpreal acos (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
262  friend const mpreal asin (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
263  friend const mpreal atan (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
264  friend const mpreal atan2 (const mpreal& y, const mpreal& x, mp_rnd_t rnd_mode = mpreal::default_rnd);
265  friend const mpreal cosh (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
266  friend const mpreal sinh (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
267  friend const mpreal tanh (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
268  friend const mpreal sech (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
269  friend const mpreal csch (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
270  friend const mpreal coth (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
271 
272  friend const mpreal acosh (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
273  friend const mpreal asinh (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
274  friend const mpreal atanh (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
275  friend const mpreal fac_ui (unsigned long int v, mp_rnd_t rnd_mode = mpreal::default_rnd);
276  friend const mpreal log1p (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
277  friend const mpreal expm1 (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
278  friend const mpreal eint (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
279 
280  friend const mpreal gamma (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
281  friend const mpreal lngamma (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
282  friend const mpreal lgamma (const mpreal& v, int *signp, mp_rnd_t rnd_mode = mpreal::default_rnd);
283  friend const mpreal zeta (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
284  friend const mpreal erf (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
285  friend const mpreal erfc (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
286  friend const mpreal _j0 (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
287  friend const mpreal _j1 (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
288  friend const mpreal _jn (long n, const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
289  friend const mpreal _y0 (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
290  friend const mpreal _y1 (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
291  friend const mpreal _yn (long n, const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
292  friend const mpreal fma (const mpreal& v1, const mpreal& v2, const mpreal& v3, mp_rnd_t rnd_mode = mpreal::default_rnd);
293  friend const mpreal fms (const mpreal& v1, const mpreal& v2, const mpreal& v3, mp_rnd_t rnd_mode = mpreal::default_rnd);
294  friend const mpreal agm (const mpreal& v1, const mpreal& v2, mp_rnd_t rnd_mode = mpreal::default_rnd);
295  friend const mpreal hypot (const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode = mpreal::default_rnd);
296  friend const mpreal sum (const mpreal tab[], unsigned long int n, mp_rnd_t rnd_mode = mpreal::default_rnd);
297  friend int sgn(const mpreal& v); // -1 or +1
298 
299 // MPFR 2.4.0 Specifics
300 #if (MPFR_VERSION >= MPFR_VERSION_NUM(2,4,0))
301  friend int sinh_cosh(mpreal& s, mpreal& c, const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
302  friend const mpreal li2(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
303  friend const mpreal fmod (const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode = mpreal::default_rnd);
304  friend const mpreal rec_sqrt(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
305 #endif
306 
307  // Exponent and mantissa manipulation
308  friend const mpreal frexp(const mpreal& v, mp_exp_t* exp);
309  friend const mpreal ldexp(const mpreal& v, mp_exp_t exp);
310 
311  // Splits mpreal value into fractional and integer parts.
312  // Returns fractional part and stores integer part in n.
313  friend const mpreal modf(const mpreal& v, mpreal& n);
314 
315  // Constants
316  // don't forget to call mpfr_free_cache() for every thread where you are using const-functions
317  friend const mpreal const_log2 (mp_prec_t prec = mpreal::default_prec, mp_rnd_t rnd_mode = mpreal::default_rnd);
318  friend const mpreal const_pi (mp_prec_t prec = mpreal::default_prec, mp_rnd_t rnd_mode = mpreal::default_rnd);
319  friend const mpreal const_euler (mp_prec_t prec = mpreal::default_prec, mp_rnd_t rnd_mode = mpreal::default_rnd);
320  friend const mpreal const_catalan (mp_prec_t prec = mpreal::default_prec, mp_rnd_t rnd_mode = mpreal::default_rnd);
321 
322  // Output/ Input
323  friend std::ostream& operator<<(std::ostream& os, const mpreal& v);
324  friend std::istream& operator>>(std::istream& is, mpreal& v);
325 
326  // Integer Related Functions
327  friend const mpreal rint (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
328  friend const mpreal ceil (const mpreal& v);
329  friend const mpreal floor(const mpreal& v);
330  friend const mpreal round(const mpreal& v);
331  friend const mpreal trunc(const mpreal& v);
332  friend const mpreal rint_ceil (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
333  friend const mpreal rint_floor(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
334  friend const mpreal rint_round(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
335  friend const mpreal rint_trunc(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
336  friend const mpreal frac (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
337  friend const mpreal remainder (const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode = mpreal::default_rnd);
338  friend const mpreal remquo (long* q, const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode = mpreal::default_rnd);
339 
340  // Miscellaneous Functions
341  friend const mpreal nexttoward (const mpreal& x, const mpreal& y);
342  friend const mpreal nextabove (const mpreal& x);
343  friend const mpreal nextbelow (const mpreal& x);
344 
345  // use gmp_randinit_default() to init state, gmp_randclear() to clear
346  friend const mpreal urandomb (gmp_randstate_t& state);
347  friend const mpreal random2 (mp_size_t size, mp_exp_t exp);
348 
349  // Instance Checkers
350  friend bool _isnan(const mpreal& v);
351  friend bool _isinf(const mpreal& v);
352  friend bool _isnum(const mpreal& v);
353  friend bool _iszero(const mpreal& v);
354  friend bool _isint(const mpreal& v);
355 
356  // Set/Get instance properties
357  mp_prec_t get_prec() const;
358  void set_prec(mp_prec_t prec, mp_rnd_t rnd_mode = default_rnd); // Change precision with rounding mode
359 
360  // Set mpreal to +-inf, NaN
361  void set_inf(int sign = +1);
362  void set_nan();
363 
364  // sign = -1 or +1
365  void set_sign(int sign, mp_rnd_t rnd_mode = default_rnd);
366 
367  //Exponent
368  mp_exp_t get_exp();
369  int set_exp(mp_exp_t e);
370  int check_range (int t, mp_rnd_t rnd_mode = default_rnd);
371  int subnormalize (int t,mp_rnd_t rnd_mode = default_rnd);
372 
373  // Inexact conversion from float
374  bool fits_in_bits(double x, int n);
375 
376  // Set/Get global properties
377  static void set_default_prec(mp_prec_t prec);
378  static mp_prec_t get_default_prec();
379  static void set_default_base(int base);
380  static int get_default_base();
381  static void set_double_bits(int dbits);
382  static int get_double_bits();
383  static void set_default_rnd(mp_rnd_t rnd_mode);
384  static mp_rnd_t get_default_rnd();
385  static mp_exp_t get_emin (void);
386  static mp_exp_t get_emax (void);
387  static mp_exp_t get_emin_min (void);
388  static mp_exp_t get_emin_max (void);
389  static mp_exp_t get_emax_min (void);
390  static mp_exp_t get_emax_max (void);
391  static int set_emin (mp_exp_t exp);
392  static int set_emax (mp_exp_t exp);
393 
394  // Get/Set conversions
395  // Convert mpreal to string with n significant digits in base b
396  // n = 0 -> convert with the maximum available digits
397  std::string to_string(size_t n = 0, int b = default_base, mp_rnd_t mode = default_rnd) const;
398 
399  // Efficient swapping of two mpreal values
400  friend void swap(mpreal& x, mpreal& y);
401 
402  //Min Max - macros is evil. Needed for systems which defines max and min globally as macros (e.g. Windows)
403  //Hope that globally defined macros uses > < operations only
404  #ifndef max
405  friend const mpreal max(const mpreal& x, const mpreal& y);
406  #endif
407 
408  #ifndef min
409  friend const mpreal min(const mpreal& x, const mpreal& y);
410  #endif
411 };
412 
414 // Exceptions
415 class conversion_overflow : public std::exception {
416 public:
417  std::string why() { return "inexact conversion from floating point"; }
418 };
419 
421 // + Addition
422 const mpreal operator+(const mpreal& a, const mpreal& b);
423 
424 // + Fast specialized addition - implemented through fast += operations
425 const mpreal operator+(const mpreal& a, const mpz_t b);
426 const mpreal operator+(const mpreal& a, const mpq_t b);
427 const mpreal operator+(const mpreal& a, const long double b);
428 const mpreal operator+(const mpreal& a, const double b);
429 const mpreal operator+(const mpreal& a, const unsigned long int b);
430 const mpreal operator+(const mpreal& a, const unsigned int b);
431 const mpreal operator+(const mpreal& a, const long int b);
432 const mpreal operator+(const mpreal& a, const int b);
433 const mpreal operator+(const mpreal& a, const char* b);
434 const mpreal operator+(const char* a, const mpreal& b);
435 const std::string operator+(const mpreal& a, const std::string b);
436 const std::string operator+(const std::string a, const mpreal& b);
437 
438 const mpreal operator+(const mpz_t b, const mpreal& a);
439 const mpreal operator+(const mpq_t b, const mpreal& a);
440 const mpreal operator+(const long double b, const mpreal& a);
441 const mpreal operator+(const double b, const mpreal& a);
442 const mpreal operator+(const unsigned long int b, const mpreal& a);
443 const mpreal operator+(const unsigned int b, const mpreal& a);
444 const mpreal operator+(const long int b, const mpreal& a);
445 const mpreal operator+(const int b, const mpreal& a);
446 
448 // - Subtraction
449 const mpreal operator-(const mpreal& a, const mpreal& b);
450 
451 // - Fast specialized subtraction - implemented through fast -= operations
452 const mpreal operator-(const mpreal& a, const mpz_t b);
453 const mpreal operator-(const mpreal& a, const mpq_t b);
454 const mpreal operator-(const mpreal& a, const long double b);
455 const mpreal operator-(const mpreal& a, const double b);
456 const mpreal operator-(const mpreal& a, const unsigned long int b);
457 const mpreal operator-(const mpreal& a, const unsigned int b);
458 const mpreal operator-(const mpreal& a, const long int b);
459 const mpreal operator-(const mpreal& a, const int b);
460 const mpreal operator-(const mpreal& a, const char* b);
461 const mpreal operator-(const char* a, const mpreal& b);
462 
463 const mpreal operator-(const mpz_t b, const mpreal& a);
464 const mpreal operator-(const mpq_t b, const mpreal& a);
465 const mpreal operator-(const long double b, const mpreal& a);
466 //const mpreal operator-(const double b, const mpreal& a);
467 
469 // * Multiplication
470 const mpreal operator*(const mpreal& a, const mpreal& b);
471 
472 // * Fast specialized multiplication - implemented through fast *= operations
473 const mpreal operator*(const mpreal& a, const mpz_t b);
474 const mpreal operator*(const mpreal& a, const mpq_t b);
475 const mpreal operator*(const mpreal& a, const long double b);
476 const mpreal operator*(const mpreal& a, const double b);
477 const mpreal operator*(const mpreal& a, const unsigned long int b);
478 const mpreal operator*(const mpreal& a, const unsigned int b);
479 const mpreal operator*(const mpreal& a, const long int b);
480 const mpreal operator*(const mpreal& a, const int b);
481 
482 const mpreal operator*(const mpz_t b, const mpreal& a);
483 const mpreal operator*(const mpq_t b, const mpreal& a);
484 const mpreal operator*(const long double b, const mpreal& a);
485 const mpreal operator*(const double b, const mpreal& a);
486 const mpreal operator*(const unsigned long int b, const mpreal& a);
487 const mpreal operator*(const unsigned int b, const mpreal& a);
488 const mpreal operator*(const long int b, const mpreal& a);
489 const mpreal operator*(const int b, const mpreal& a);
490 
492 // / Division
493 const mpreal operator/(const mpreal& a, const mpreal& b);
494 
495 // / Fast specialized division - implemented through fast /= operations
496 const mpreal operator/(const mpreal& a, const mpz_t b);
497 const mpreal operator/(const mpreal& a, const mpq_t b);
498 const mpreal operator/(const mpreal& a, const long double b);
499 const mpreal operator/(const mpreal& a, const double b);
500 const mpreal operator/(const mpreal& a, const unsigned long int b);
501 const mpreal operator/(const mpreal& a, const unsigned int b);
502 const mpreal operator/(const mpreal& a, const long int b);
503 const mpreal operator/(const mpreal& a, const int b);
504 
505 const mpreal operator/(const long double b, const mpreal& a);
506 
508 // Shifts operators - Multiplication/Division by a power of 2
509 const mpreal operator<<(const mpreal& v, const unsigned long int k);
510 const mpreal operator<<(const mpreal& v, const unsigned int k);
511 const mpreal operator<<(const mpreal& v, const long int k);
512 const mpreal operator<<(const mpreal& v, const int k);
513 
514 const mpreal operator>>(const mpreal& v, const unsigned long int k);
515 const mpreal operator>>(const mpreal& v, const unsigned int k);
516 const mpreal operator>>(const mpreal& v, const long int k);
517 const mpreal operator>>(const mpreal& v, const int k);
518 
520 // Boolean operators
521 bool operator < (const mpreal& a, const unsigned long int b);
522 bool operator < (const mpreal& a, const unsigned int b);
523 bool operator < (const mpreal& a, const long int b);
524 bool operator < (const mpreal& a, const int b);
525 bool operator < (const mpreal& a, const long double b);
526 bool operator < (const mpreal& a, const double b);
527 
528 bool operator < (const unsigned long int a,const mpreal& b);
529 bool operator < (const unsigned int a, const mpreal& b);
530 bool operator < (const long int a, const mpreal& b);
531 bool operator < (const int a, const mpreal& b);
532 bool operator < (const long double a, const mpreal& b);
533 bool operator < (const double a, const mpreal& b);
534 
535 bool operator > (const mpreal& a, const unsigned long int b);
536 bool operator > (const mpreal& a, const unsigned int b);
537 bool operator > (const mpreal& a, const long int b);
538 bool operator > (const mpreal& a, const int b);
539 bool operator > (const mpreal& a, const long double b);
540 bool operator > (const mpreal& a, const double b);
541 
542 bool operator > (const unsigned long int a,const mpreal& b);
543 bool operator > (const unsigned int a, const mpreal& b);
544 bool operator > (const long int a, const mpreal& b);
545 bool operator > (const int a, const mpreal& b);
546 bool operator > (const long double a, const mpreal& b);
547 bool operator > (const double a, const mpreal& b);
548 
549 bool operator >= (const mpreal& a, const unsigned long int b);
550 bool operator >= (const mpreal& a, const unsigned int b);
551 bool operator >= (const mpreal& a, const long int b);
552 bool operator >= (const mpreal& a, const int b);
553 bool operator >= (const mpreal& a, const long double b);
554 bool operator >= (const mpreal& a, const double b);
555 
556 bool operator >= (const unsigned long int a,const mpreal& b);
557 bool operator >= (const unsigned int a, const mpreal& b);
558 bool operator >= (const long int a, const mpreal& b);
559 bool operator >= (const int a, const mpreal& b);
560 bool operator >= (const long double a, const mpreal& b);
561 bool operator >= (const double a, const mpreal& b);
562 
563 bool operator <= (const mpreal& a, const unsigned long int b);
564 bool operator <= (const mpreal& a, const unsigned int b);
565 bool operator <= (const mpreal& a, const long int b);
566 bool operator <= (const mpreal& a, const int b);
567 bool operator <= (const mpreal& a, const long double b);
568 bool operator <= (const mpreal& a, const double b);
569 
570 bool operator <= (const unsigned long int a,const mpreal& b);
571 bool operator <= (const unsigned int a, const mpreal& b);
572 bool operator <= (const long int a, const mpreal& b);
573 bool operator <= (const int a, const mpreal& b);
574 bool operator <= (const long double a, const mpreal& b);
575 bool operator <= (const double a, const mpreal& b);
576 
577 bool operator == (const mpreal& a, const unsigned long int b);
578 bool operator == (const mpreal& a, const unsigned int b);
579 bool operator == (const mpreal& a, const long int b);
580 bool operator == (const mpreal& a, const int b);
581 bool operator == (const mpreal& a, const long double b);
582 bool operator == (const mpreal& a, const double b);
583 
584 bool operator == (const unsigned long int a,const mpreal& b);
585 bool operator == (const unsigned int a, const mpreal& b);
586 bool operator == (const long int a, const mpreal& b);
587 bool operator == (const int a, const mpreal& b);
588 bool operator == (const long double a, const mpreal& b);
589 bool operator == (const double a, const mpreal& b);
590 
591 bool operator != (const mpreal& a, const unsigned long int b);
592 bool operator != (const mpreal& a, const unsigned int b);
593 bool operator != (const mpreal& a, const long int b);
594 bool operator != (const mpreal& a, const int b);
595 bool operator != (const mpreal& a, const long double b);
596 bool operator != (const mpreal& a, const double b);
597 
598 bool operator != (const unsigned long int a,const mpreal& b);
599 bool operator != (const unsigned int a, const mpreal& b);
600 bool operator != (const long int a, const mpreal& b);
601 bool operator != (const int a, const mpreal& b);
602 bool operator != (const long double a, const mpreal& b);
603 bool operator != (const double a, const mpreal& b);
604 
606 // sqrt
607 const mpreal sqrt(const unsigned int v, mp_rnd_t rnd_mode = mpreal::default_rnd);
608 const mpreal sqrt(const long int v, mp_rnd_t rnd_mode = mpreal::default_rnd);
609 const mpreal sqrt(const int v, mp_rnd_t rnd_mode = mpreal::default_rnd);
610 const mpreal sqrt(const long double v, mp_rnd_t rnd_mode = mpreal::default_rnd);
611 const mpreal sqrt(const double v, mp_rnd_t rnd_mode = mpreal::default_rnd);
612 
614 // pow
615 const mpreal pow(const mpreal& a, const unsigned int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
616 const mpreal pow(const mpreal& a, const int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
617 const mpreal pow(const mpreal& a, const long double b, mp_rnd_t rnd_mode = mpreal::default_rnd);
618 const mpreal pow(const mpreal& a, const double b, mp_rnd_t rnd_mode = mpreal::default_rnd);
619 
620 const mpreal pow(const unsigned int a, const mpreal& b, mp_rnd_t rnd_mode = mpreal::default_rnd);
621 const mpreal pow(const long int a, const mpreal& b, mp_rnd_t rnd_mode = mpreal::default_rnd);
622 const mpreal pow(const int a, const mpreal& b, mp_rnd_t rnd_mode = mpreal::default_rnd);
623 const mpreal pow(const long double a, const mpreal& b, mp_rnd_t rnd_mode = mpreal::default_rnd);
624 const mpreal pow(const double a, const mpreal& b, mp_rnd_t rnd_mode = mpreal::default_rnd);
625 
626 const mpreal pow(const unsigned long int a, const unsigned int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
627 const mpreal pow(const unsigned long int a, const long int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
628 const mpreal pow(const unsigned long int a, const int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
629 const mpreal pow(const unsigned long int a, const long double b, mp_rnd_t rnd_mode = mpreal::default_rnd);
630 const mpreal pow(const unsigned long int a, const double b, mp_rnd_t rnd_mode = mpreal::default_rnd);
631 
632 const mpreal pow(const unsigned int a, const unsigned long int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
633 const mpreal pow(const unsigned int a, const unsigned int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
634 const mpreal pow(const unsigned int a, const long int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
635 const mpreal pow(const unsigned int a, const int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
636 const mpreal pow(const unsigned int a, const long double b, mp_rnd_t rnd_mode = mpreal::default_rnd);
637 const mpreal pow(const unsigned int a, const double b, mp_rnd_t rnd_mode = mpreal::default_rnd);
638 
639 const mpreal pow(const long int a, const unsigned long int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
640 const mpreal pow(const long int a, const unsigned int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
641 const mpreal pow(const long int a, const long int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
642 const mpreal pow(const long int a, const int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
643 const mpreal pow(const long int a, const long double b, mp_rnd_t rnd_mode = mpreal::default_rnd);
644 const mpreal pow(const long int a, const double b, mp_rnd_t rnd_mode = mpreal::default_rnd);
645 
646 const mpreal pow(const int a, const unsigned long int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
647 const mpreal pow(const int a, const unsigned int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
648 const mpreal pow(const int a, const long int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
649 const mpreal pow(const int a, const int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
650 const mpreal pow(const int a, const long double b, mp_rnd_t rnd_mode = mpreal::default_rnd);
651 const mpreal pow(const int a, const double b, mp_rnd_t rnd_mode = mpreal::default_rnd);
652 
653 const mpreal pow(const long double a, const long double b, mp_rnd_t rnd_mode = mpreal::default_rnd);
654 const mpreal pow(const long double a, const unsigned long int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
655 const mpreal pow(const long double a, const unsigned int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
656 const mpreal pow(const long double a, const long int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
657 const mpreal pow(const long double a, const int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
658 
659 const mpreal pow(const double a, const double b, mp_rnd_t rnd_mode = mpreal::default_rnd);
660 const mpreal pow(const double a, const unsigned long int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
661 const mpreal pow(const double a, const unsigned int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
662 const mpreal pow(const double a, const long int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
663 const mpreal pow(const double a, const int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
664 
666 // Implementation of inline functions
668 
670 // Operators - Assignment
671 inline mpreal& mpreal::operator=(const mpreal& v)
672 {
673  if (this!= &v) mpfr_set(mp,v.mp,default_rnd);
674  return *this;
675 }
676 
677 inline mpreal& mpreal::operator=(const mpf_t v)
678 {
679  mpfr_set_f(mp,v,default_rnd);
680  return *this;
681 }
682 
683 inline mpreal& mpreal::operator=(const mpz_t v)
684 {
685  mpfr_set_z(mp,v,default_rnd);
686  return *this;
687 }
688 
689 inline mpreal& mpreal::operator=(const mpq_t v)
690 {
691  mpfr_set_q(mp,v,default_rnd);
692  return *this;
693 }
694 
695 inline mpreal& mpreal::operator=(const long double v)
696 {
697  mpfr_set_ld(mp,v,default_rnd);
698  return *this;
699 }
700 
701 inline mpreal& mpreal::operator=(const double v)
702 {
703  if(double_bits == -1 || fits_in_bits(v, double_bits))
704  {
705  mpfr_set_d(mp,v,default_rnd);
706  }
707  else
708  throw conversion_overflow();
709 
710  return *this;
711 }
712 
713 inline mpreal& mpreal::operator=(const unsigned long int v)
714 {
715  mpfr_set_ui(mp,v,default_rnd);
716  return *this;
717 }
718 
719 inline mpreal& mpreal::operator=(const unsigned int v)
720 {
721  mpfr_set_ui(mp,v,default_rnd);
722  return *this;
723 }
724 
725 inline mpreal& mpreal::operator=(const long int v)
726 {
727  mpfr_set_si(mp,v,default_rnd);
728  return *this;
729 }
730 
731 inline mpreal& mpreal::operator=(const int v)
732 {
733  mpfr_set_si(mp,v,default_rnd);
734  return *this;
735 }
736 
738 // + Addition
739 inline mpreal& mpreal::operator+=(const mpreal& v)
740 {
741  mpfr_add(mp,mp,v.mp,default_rnd);
742  return *this;
743 }
744 
745 inline mpreal& mpreal::operator+=(const mpf_t u)
746 {
747  *this += mpreal(u);
748  return *this;
749 }
750 
751 inline mpreal& mpreal::operator+=(const mpz_t u)
752 {
753  mpfr_add_z(mp,mp,u,default_rnd);
754  return *this;
755 }
756 
757 inline mpreal& mpreal::operator+=(const mpq_t u)
758 {
759  mpfr_add_q(mp,mp,u,default_rnd);
760  return *this;
761 }
762 
763 inline mpreal& mpreal::operator+= (const long double u)
764 {
765  return *this += mpreal(u);
766 }
767 
768 inline mpreal& mpreal::operator+= (const double u)
769 {
770 #if (MPFR_VERSION >= MPFR_VERSION_NUM(2,4,0))
771  mpfr_add_d(mp,mp,u,default_rnd);
772  return *this;
773 #else
774  return *this += mpreal(u);
775 #endif
776 }
777 
778 inline mpreal& mpreal::operator+=(const unsigned long int u)
779 {
780  mpfr_add_ui(mp,mp,u,default_rnd);
781  return *this;
782 }
783 
784 inline mpreal& mpreal::operator+=(const unsigned int u)
785 {
786  mpfr_add_ui(mp,mp,u,default_rnd);
787  return *this;
788 }
789 
790 inline mpreal& mpreal::operator+=(const long int u)
791 {
792  mpfr_add_si(mp,mp,u,default_rnd);
793  return *this;
794 }
795 
796 inline mpreal& mpreal::operator+=(const int u)
797 {
798  mpfr_add_si(mp,mp,u,default_rnd);
799  return *this;
800 }
801 
802 inline const mpreal mpreal::operator+()const
803 {
804  return mpreal(*this);
805 }
806 
807 inline const mpreal operator+(const mpreal& a, const mpreal& b)
808 {
809  // prec(a+b) = max(prec(a),prec(b))
810  if(a.get_prec()>b.get_prec()) return mpreal(a) += b;
811  else return mpreal(b) += a;
812 }
813 
814 inline const std::string operator+(const mpreal& a, const std::string b)
815 {
816  return (std::string)a+b;
817 }
818 
819 inline const std::string operator+(const std::string a, const mpreal& b)
820 {
821  return a+(std::string)b;
822 }
823 
824 inline const mpreal operator+(const mpreal& a, const mpz_t b)
825 {
826  return mpreal(a) += b;
827 }
828 
829 inline const mpreal operator+(const mpreal& a, const char* b)
830 {
831  return a+mpreal(b);
832 }
833 
834 inline const mpreal operator+(const char* a, const mpreal& b)
835 {
836  return mpreal(a)+b;
837 
838 }
839 
840 inline const mpreal operator+(const mpreal& a, const mpq_t b)
841 {
842  return mpreal(a) += b;
843 }
844 
845 inline const mpreal operator+(const mpreal& a, const long double b)
846 {
847  return mpreal(a) += b;
848 }
849 
850 inline const mpreal operator+(const mpreal& a, const double b)
851 {
852  return mpreal(a) += b;
853 }
854 
855 inline const mpreal operator+(const mpreal& a, const unsigned long int b)
856 {
857  return mpreal(a) += b;
858 }
859 
860 inline const mpreal operator+(const mpreal& a, const unsigned int b)
861 {
862  return mpreal(a) += b;
863 }
864 
865 inline const mpreal operator+(const mpreal& a, const long int b)
866 {
867  return mpreal(a) += b;
868 }
869 
870 inline const mpreal operator+(const mpreal& a, const int b)
871 {
872  return mpreal(a) += b;
873 }
874 
875 inline const mpreal operator+(const mpz_t b, const mpreal& a)
876 {
877  return mpreal(a) += b;
878 }
879 
880 inline const mpreal operator+(const mpq_t b, const mpreal& a)
881 {
882  return mpreal(a) += b;
883 }
884 
885 inline const mpreal operator+(const long double b, const mpreal& a)
886 {
887  return mpreal(a) += b;
888 }
889 
890 inline const mpreal operator+(const double b, const mpreal& a)
891 {
892  return mpreal(a) += b;
893 }
894 
895 inline const mpreal operator+(const unsigned long int b, const mpreal& a)
896 {
897  return mpreal(a) += b;
898 }
899 
900 inline const mpreal operator+(const unsigned int b, const mpreal& a)
901 {
902  return mpreal(a) += b;
903 }
904 
905 inline const mpreal operator+(const long int b, const mpreal& a)
906 {
907  return mpreal(a) += b;
908 }
909 
910 inline const mpreal operator+(const int b, const mpreal& a)
911 {
912  return mpreal(a) += b;
913 }
914 
915 inline mpreal& mpreal::operator++()
916 {
917  *this += 1;
918  return *this;
919 }
920 
921 inline const mpreal mpreal::operator++ (int)
922 {
923  mpreal x(*this);
924  *this += 1;
925  return x;
926 }
927 
928 inline mpreal& mpreal::operator--()
929 {
930  *this -= 1;
931  return *this;
932 }
933 
934 inline const mpreal mpreal::operator-- (int)
935 {
936  mpreal x(*this);
937  *this -= 1;
938  return x;
939 }
940 
942 // - Subtraction
943 inline mpreal& mpreal::operator-= (const mpreal& v)
944 {
945  mpfr_sub(mp,mp,v.mp,default_rnd);
946  return *this;
947 }
948 
949 inline mpreal& mpreal::operator-=(const mpz_t v)
950 {
951  mpfr_sub_z(mp,mp,v,default_rnd);
952  return *this;
953 }
954 
955 inline mpreal& mpreal::operator-=(const mpq_t v)
956 {
957  mpfr_sub_q(mp,mp,v,default_rnd);
958  return *this;
959 }
960 
961 inline mpreal& mpreal::operator-=(const long double v)
962 {
963  return *this -= mpreal(v);
964 }
965 
966 inline mpreal& mpreal::operator-=(const double v)
967 {
968 #if (MPFR_VERSION >= MPFR_VERSION_NUM(2,4,0))
969  mpfr_sub_d(mp,mp,v,default_rnd);
970  return *this;
971 #else
972  return *this -= mpreal(v);
973 #endif
974 }
975 
976 inline mpreal& mpreal::operator-=(const unsigned long int v)
977 {
978  mpfr_sub_ui(mp,mp,v,default_rnd);
979  return *this;
980 }
981 
982 inline mpreal& mpreal::operator-=(const unsigned int v)
983 {
984  mpfr_sub_ui(mp,mp,v,default_rnd);
985  return *this;
986 }
987 
988 inline mpreal& mpreal::operator-=(const long int v)
989 {
990  mpfr_sub_si(mp,mp,v,default_rnd);
991  return *this;
992 }
993 
994 inline mpreal& mpreal::operator-=(const int v)
995 {
996  mpfr_sub_si(mp,mp,v,default_rnd);
997  return *this;
998 }
999 
1000 inline const mpreal mpreal::operator-()const
1001 {
1002  mpreal u(*this);
1003  mpfr_neg(u.mp,u.mp,default_rnd);
1004  return u;
1005 }
1006 
1007 inline const mpreal operator-(const mpreal& a, const mpreal& b)
1008 {
1009  // prec(a-b) = max(prec(a),prec(b))
1010  if(a.get_prec()>b.get_prec()) return mpreal(a) -= b;
1011  else return -(mpreal(b) -= a);
1012 }
1013 
1014 inline const mpreal operator-(const mpreal& a, const mpz_t b)
1015 {
1016  return mpreal(a) -= b;
1017 }
1018 
1019 inline const mpreal operator-(const mpreal& a, const mpq_t b)
1020 {
1021  return mpreal(a) -= b;
1022 }
1023 
1024 inline const mpreal operator-(const mpreal& a, const long double b)
1025 {
1026  return mpreal(a) -= b;
1027 }
1028 
1029 inline const mpreal operator-(const mpreal& a, const double b)
1030 {
1031  return mpreal(a) -= b;
1032 }
1033 
1034 inline const mpreal operator-(const mpreal& a, const unsigned long int b)
1035 {
1036  return mpreal(a) -= b;
1037 }
1038 
1039 inline const mpreal operator-(const mpreal& a, const unsigned int b)
1040 {
1041  return mpreal(a) -= b;
1042 }
1043 
1044 inline const mpreal operator-(const mpreal& a, const long int b)
1045 {
1046  return mpreal(a) -= b;
1047 }
1048 
1049 inline const mpreal operator-(const mpreal& a, const int b)
1050 {
1051  return mpreal(a) -= b;
1052 }
1053 
1054 inline const mpreal operator-(const mpz_t b, const mpreal& a)
1055 {
1056  return -(mpreal(a) -= b);
1057 }
1058 
1059 inline const mpreal operator-(const mpq_t b, const mpreal& a)
1060 {
1061  return -(mpreal(a) -= b);
1062 }
1063 
1064 inline const mpreal operator-(const long double b, const mpreal& a)
1065 {
1066  return -(mpreal(a) -= b);
1067 }
1068 
1069 inline const mpreal operator-(const double b, const mpreal& a)
1070 {
1071 #if (MPFR_VERSION >= MPFR_VERSION_NUM(2,4,0))
1072  mpreal x(a);
1073  mpfr_d_sub(x.mp,b,a.mp,mpreal::default_rnd);
1074  return x;
1075 #else
1076  return -(mpreal(a) -= b);
1077 #endif
1078 }
1079 
1080 inline const mpreal operator-(const unsigned long int b, const mpreal& a)
1081 {
1082  mpreal x(a);
1083  mpfr_ui_sub(x.mp,b,a.mp,mpreal::default_rnd);
1084  return x;
1085 }
1086 
1087 inline const mpreal operator-(const unsigned int b, const mpreal& a)
1088 {
1089  mpreal x(a);
1090  mpfr_ui_sub(x.mp,b,a.mp,mpreal::default_rnd);
1091  return x;
1092 }
1093 
1094 inline const mpreal operator-(const long int b, const mpreal& a)
1095 {
1096  mpreal x(a);
1097  mpfr_si_sub(x.mp,b,a.mp,mpreal::default_rnd);
1098  return x;
1099 }
1100 
1101 inline const mpreal operator-(const int b, const mpreal& a)
1102 {
1103  mpreal x(a);
1104  mpfr_si_sub(x.mp,b,a.mp,mpreal::default_rnd);
1105  return x;
1106 }
1107 
1108 inline const mpreal operator-(const mpreal& a, const char* b)
1109 {
1110  return a-mpreal(b);
1111 }
1112 
1113 inline const mpreal operator-(const char* a, const mpreal& b)
1114 {
1115  return mpreal(a)-b;
1116 }
1117 
1119 // * Multiplication
1120 inline mpreal& mpreal::operator*= (const mpreal& v)
1121 {
1122  mpfr_mul(mp,mp,v.mp,default_rnd);
1123  return *this;
1124 }
1125 
1126 inline mpreal& mpreal::operator*=(const mpz_t v)
1127 {
1128  mpfr_mul_z(mp,mp,v,default_rnd);
1129  return *this;
1130 }
1131 
1132 inline mpreal& mpreal::operator*=(const mpq_t v)
1133 {
1134  mpfr_mul_q(mp,mp,v,default_rnd);
1135  return *this;
1136 }
1137 
1138 inline mpreal& mpreal::operator*=(const long double v)
1139 {
1140  return *this *= mpreal(v);
1141 }
1142 
1143 inline mpreal& mpreal::operator*=(const double v)
1144 {
1145 #if (MPFR_VERSION >= MPFR_VERSION_NUM(2,4,0))
1146  mpfr_mul_d(mp,mp,v,default_rnd);
1147  return *this;
1148 #else
1149  return *this *= mpreal(v);
1150 #endif
1151 }
1152 
1153 inline mpreal& mpreal::operator*=(const unsigned long int v)
1154 {
1155  mpfr_mul_ui(mp,mp,v,default_rnd);
1156  return *this;
1157 }
1158 
1159 inline mpreal& mpreal::operator*=(const unsigned int v)
1160 {
1161  mpfr_mul_ui(mp,mp,v,default_rnd);
1162  return *this;
1163 }
1164 
1165 inline mpreal& mpreal::operator*=(const long int v)
1166 {
1167  mpfr_mul_si(mp,mp,v,default_rnd);
1168  return *this;
1169 }
1170 
1171 inline mpreal& mpreal::operator*=(const int v)
1172 {
1173  mpfr_mul_si(mp,mp,v,default_rnd);
1174  return *this;
1175 }
1176 
1177 inline const mpreal operator*(const mpreal& a, const mpreal& b)
1178 {
1179  // prec(a*b) = max(prec(a),prec(b))
1180  if(a.get_prec()>b.get_prec()) return mpreal(a) *= b;
1181  else return mpreal(b) *= a;
1182 }
1183 
1184 inline const mpreal operator*(const mpreal& a, const mpz_t b)
1185 {
1186  return mpreal(a) *= b;
1187 }
1188 
1189 inline const mpreal operator*(const mpreal& a, const mpq_t b)
1190 {
1191  return mpreal(a) *= b;
1192 }
1193 
1194 inline const mpreal operator*(const mpreal& a, const long double b)
1195 {
1196  return mpreal(a) *= b;
1197 }
1198 
1199 inline const mpreal operator*(const mpreal& a, const double b)
1200 {
1201  return mpreal(a) *= b;
1202 }
1203 
1204 inline const mpreal operator*(const mpreal& a, const unsigned long int b)
1205 {
1206  return mpreal(a) *= b;
1207 }
1208 
1209 inline const mpreal operator*(const mpreal& a, const unsigned int b)
1210 {
1211  return mpreal(a) *= b;
1212 }
1213 
1214 inline const mpreal operator*(const mpreal& a, const long int b)
1215 {
1216  return mpreal(a) *= b;
1217 }
1218 
1219 inline const mpreal operator*(const mpreal& a, const int b)
1220 {
1221  return mpreal(a) *= b;
1222 }
1223 
1224 inline const mpreal operator*(const mpz_t b, const mpreal& a)
1225 {
1226  return mpreal(a) *= b;
1227 }
1228 
1229 inline const mpreal operator*(const mpq_t b, const mpreal& a)
1230 {
1231  return mpreal(a) *= b;
1232 }
1233 
1234 inline const mpreal operator*(const long double b, const mpreal& a)
1235 {
1236  return mpreal(a) *= b;
1237 }
1238 
1239 inline const mpreal operator*(const double b, const mpreal& a)
1240 {
1241  return mpreal(a) *= b;
1242 }
1243 
1244 inline const mpreal operator*(const unsigned long int b, const mpreal& a)
1245 {
1246  return mpreal(a) *= b;
1247 }
1248 
1249 inline const mpreal operator*(const unsigned int b, const mpreal& a)
1250 {
1251  return mpreal(a) *= b;
1252 }
1253 
1254 inline const mpreal operator*(const long int b, const mpreal& a)
1255 {
1256  return mpreal(a) *= b;
1257 }
1258 
1259 inline const mpreal operator*(const int b, const mpreal& a)
1260 {
1261  return mpreal(a) *= b;
1262 }
1263 
1265 // / Division
1266 inline mpreal& mpreal::operator/=(const mpreal& v)
1267 {
1268  mpfr_div(mp,mp,v.mp,default_rnd);
1269  return *this;
1270 }
1271 
1272 inline mpreal& mpreal::operator/=(const mpz_t v)
1273 {
1274  mpfr_div_z(mp,mp,v,default_rnd);
1275  return *this;
1276 }
1277 
1278 inline mpreal& mpreal::operator/=(const mpq_t v)
1279 {
1280  mpfr_div_q(mp,mp,v,default_rnd);
1281  return *this;
1282 }
1283 
1284 inline mpreal& mpreal::operator/=(const long double v)
1285 {
1286  return *this /= mpreal(v);
1287 }
1288 
1289 inline mpreal& mpreal::operator/=(const double v)
1290 {
1291 #if (MPFR_VERSION >= MPFR_VERSION_NUM(2,4,0))
1292  mpfr_div_d(mp,mp,v,default_rnd);
1293  return *this;
1294 #else
1295  return *this /= mpreal(v);
1296 #endif
1297 }
1298 
1299 inline mpreal& mpreal::operator/=(const unsigned long int v)
1300 {
1301  mpfr_div_ui(mp,mp,v,default_rnd);
1302  return *this;
1303 }
1304 
1305 inline mpreal& mpreal::operator/=(const unsigned int v)
1306 {
1307  mpfr_div_ui(mp,mp,v,default_rnd);
1308  return *this;
1309 }
1310 
1311 inline mpreal& mpreal::operator/=(const long int v)
1312 {
1313  mpfr_div_si(mp,mp,v,default_rnd);
1314  return *this;
1315 }
1316 
1317 inline mpreal& mpreal::operator/=(const int v)
1318 {
1319  mpfr_div_si(mp,mp,v,default_rnd);
1320  return *this;
1321 }
1322 
1323 inline const mpreal operator/(const mpreal& a, const mpreal& b)
1324 {
1325  mpreal x(a);
1326  mp_prec_t pb;
1327  mp_prec_t pa;
1328 
1329  // prec(a/b) = max(prec(a),prec(b))
1330  pa = a.get_prec();
1331  pb = b.get_prec();
1332  if(pb>pa) x.set_prec(pb);
1333 
1334  return x /= b;
1335 }
1336 
1337 inline const mpreal operator/(const mpreal& a, const mpz_t b)
1338 {
1339  return mpreal(a) /= b;
1340 }
1341 
1342 inline const mpreal operator/(const mpreal& a, const mpq_t b)
1343 {
1344  return mpreal(a) /= b;
1345 }
1346 
1347 inline const mpreal operator/(const mpreal& a, const long double b)
1348 {
1349  return mpreal(a) /= b;
1350 }
1351 
1352 inline const mpreal operator/(const mpreal& a, const double b)
1353 {
1354  return mpreal(a) /= b;
1355 }
1356 
1357 inline const mpreal operator/(const mpreal& a, const unsigned long int b)
1358 {
1359  return mpreal(a) /= b;
1360 }
1361 
1362 inline const mpreal operator/(const mpreal& a, const unsigned int b)
1363 {
1364  return mpreal(a) /= b;
1365 }
1366 
1367 inline const mpreal operator/(const mpreal& a, const long int b)
1368 {
1369  return mpreal(a) /= b;
1370 }
1371 
1372 inline const mpreal operator/(const mpreal& a, const int b)
1373 {
1374  return mpreal(a) /= b;
1375 }
1376 
1377 inline const mpreal operator/(const unsigned long int b, const mpreal& a)
1378 {
1379  mpreal x(a);
1380  mpfr_ui_div(x.mp,b,a.mp,mpreal::default_rnd);
1381  return x;
1382 }
1383 
1384 inline const mpreal operator/(const unsigned int b, const mpreal& a)
1385 {
1386  mpreal x(a);
1387  mpfr_ui_div(x.mp,b,a.mp,mpreal::default_rnd);
1388  return x;
1389 }
1390 
1391 inline const mpreal operator/(const long int b, const mpreal& a)
1392 {
1393  mpreal x(a);
1394  mpfr_si_div(x.mp,b,a.mp,mpreal::default_rnd);
1395  return x;
1396 }
1397 
1398 inline const mpreal operator/(const int b, const mpreal& a)
1399 {
1400  mpreal x(a);
1401  mpfr_si_div(x.mp,b,a.mp,mpreal::default_rnd);
1402  return x;
1403 }
1404 
1405 inline const mpreal operator/(const long double b, const mpreal& a)
1406 {
1407  mpreal x(b);
1408  return x/a;
1409 }
1410 
1411 inline const mpreal operator/(const double b, const mpreal& a)
1412 {
1413 #if (MPFR_VERSION >= MPFR_VERSION_NUM(2,4,0))
1414  mpreal x(a);
1415  mpfr_d_div(x.mp,b,a.mp,mpreal::default_rnd);
1416  return x;
1417 #else
1418  mpreal x(b);
1419  return x/a;
1420 #endif
1421 }
1422 
1424 // Shifts operators - Multiplication/Division by power of 2
1425 inline mpreal& mpreal::operator<<=(const unsigned long int u)
1426 {
1427  mpfr_mul_2ui(mp,mp,u,default_rnd);
1428  return *this;
1429 }
1430 
1431 inline mpreal& mpreal::operator<<=(const unsigned int u)
1432 {
1433  mpfr_mul_2ui(mp,mp,static_cast<unsigned long int>(u),default_rnd);
1434  return *this;
1435 }
1436 
1437 inline mpreal& mpreal::operator<<=(const long int u)
1438 {
1439  mpfr_mul_2si(mp,mp,u,default_rnd);
1440  return *this;
1441 }
1442 
1443 inline mpreal& mpreal::operator<<=(const int u)
1444 {
1445  mpfr_mul_2si(mp,mp,static_cast<long int>(u),default_rnd);
1446  return *this;
1447 }
1448 
1449 inline mpreal& mpreal::operator>>=(const unsigned long int u)
1450 {
1451  mpfr_div_2ui(mp,mp,u,default_rnd);
1452  return *this;
1453 }
1454 
1455 inline mpreal& mpreal::operator>>=(const unsigned int u)
1456 {
1457  mpfr_div_2ui(mp,mp,static_cast<unsigned long int>(u),default_rnd);
1458  return *this;
1459 }
1460 
1461 inline mpreal& mpreal::operator>>=(const long int u)
1462 {
1463  mpfr_div_2si(mp,mp,u,default_rnd);
1464  return *this;
1465 }
1466 
1467 inline mpreal& mpreal::operator>>=(const int u)
1468 {
1469  mpfr_div_2si(mp,mp,static_cast<long int>(u),default_rnd);
1470  return *this;
1471 }
1472 
1473 inline const mpreal operator<<(const mpreal& v, const unsigned long int k)
1474 {
1475  return mul_2ui(v,k);
1476 }
1477 
1478 inline const mpreal operator<<(const mpreal& v, const unsigned int k)
1479 {
1480  return mul_2ui(v,static_cast<unsigned long int>(k));
1481 }
1482 
1483 inline const mpreal operator<<(const mpreal& v, const long int k)
1484 {
1485  return mul_2si(v,k);
1486 }
1487 
1488 inline const mpreal operator<<(const mpreal& v, const int k)
1489 {
1490  return mul_2si(v,static_cast<long int>(k));
1491 }
1492 
1493 inline const mpreal operator>>(const mpreal& v, const unsigned long int k)
1494 {
1495  return div_2ui(v,k);
1496 }
1497 
1498 inline const mpreal operator>>(const mpreal& v, const long int k)
1499 {
1500  return div_2si(v,k);
1501 }
1502 
1503 inline const mpreal operator>>(const mpreal& v, const unsigned int k)
1504 {
1505  return div_2ui(v,static_cast<unsigned long int>(k));
1506 }
1507 
1508 inline const mpreal operator>>(const mpreal& v, const int k)
1509 {
1510  return div_2si(v,static_cast<long int>(k));
1511 }
1512 
1513 // mul_2ui
1514 inline const mpreal mul_2ui(const mpreal& v, unsigned long int k, mp_rnd_t rnd_mode)
1515 {
1516  mpreal x(v);
1517  mpfr_mul_2ui(x.mp,v.mp,k,rnd_mode);
1518  return x;
1519 }
1520 
1521 // mul_2si
1522 inline const mpreal mul_2si(const mpreal& v, long int k, mp_rnd_t rnd_mode)
1523 {
1524  mpreal x(v);
1525  mpfr_mul_2si(x.mp,v.mp,k,rnd_mode);
1526  return x;
1527 }
1528 
1529 inline const mpreal div_2ui(const mpreal& v, unsigned long int k, mp_rnd_t rnd_mode)
1530 {
1531  mpreal x(v);
1532  mpfr_div_2ui(x.mp,v.mp,k,rnd_mode);
1533  return x;
1534 }
1535 
1536 inline const mpreal div_2si(const mpreal& v, long int k, mp_rnd_t rnd_mode)
1537 {
1538  mpreal x(v);
1539  mpfr_div_2si(x.mp,v.mp,k,rnd_mode);
1540  return x;
1541 }
1542 
1544 //Boolean operators
1545 inline bool operator > (const mpreal& a, const mpreal& b)
1546 {
1547  return (mpfr_greater_p(a.mp,b.mp)!=0);
1548 }
1549 
1550 inline bool operator > (const mpreal& a, const unsigned long int b)
1551 {
1552  return a>mpreal(b);
1553 }
1554 
1555 inline bool operator > (const mpreal& a, const unsigned int b)
1556 {
1557  return a>mpreal(b);
1558 }
1559 
1560 inline bool operator > (const mpreal& a, const long int b)
1561 {
1562  return a>mpreal(b);
1563 }
1564 
1565 inline bool operator > (const mpreal& a, const int b)
1566 {
1567  return a>mpreal(b);
1568 }
1569 
1570 inline bool operator > (const mpreal& a, const long double b)
1571 {
1572  return a>mpreal(b);
1573 }
1574 
1575 inline bool operator > (const mpreal& a, const double b)
1576 {
1577  return a>mpreal(b);
1578 }
1579 
1580 inline bool operator > (const unsigned long int a, const mpreal& b)
1581 {
1582  return mpreal(a)>b;
1583 }
1584 
1585 inline bool operator > (const unsigned int a, const mpreal& b)
1586 {
1587  return mpreal(a)>b;
1588 }
1589 
1590 inline bool operator > (const long int a, const mpreal& b)
1591 {
1592  return mpreal(a)>b;
1593 }
1594 
1595 inline bool operator > (const int a, const mpreal& b)
1596 {
1597  return mpreal(a)>b;
1598 }
1599 
1600 inline bool operator > (const long double a, const mpreal& b)
1601 {
1602  return mpreal(a)>b;
1603 }
1604 
1605 inline bool operator > (const double a, const mpreal& b)
1606 {
1607  return mpreal(a)>b;
1608 }
1609 
1610 inline bool operator >= (const mpreal& a, const mpreal& b)
1611 {
1612  return (mpfr_greaterequal_p(a.mp,b.mp)!=0);
1613 }
1614 
1615 inline bool operator >= (const mpreal& a, const unsigned long int b)
1616 {
1617  return a>=mpreal(b);
1618 }
1619 
1620 inline bool operator >= (const mpreal& a, const unsigned int b)
1621 {
1622  return a>=mpreal(b);
1623 }
1624 
1625 inline bool operator >= (const mpreal& a, const long int b)
1626 {
1627  return a>=mpreal(b);
1628 }
1629 
1630 inline bool operator >= (const mpreal& a, const int b)
1631 {
1632  return a>=mpreal(b);
1633 }
1634 
1635 inline bool operator >= (const mpreal& a, const long double b)
1636 {
1637  return a>=mpreal(b);
1638 }
1639 
1640 inline bool operator >= (const mpreal& a, const double b)
1641 {
1642  return a>=mpreal(b);
1643 }
1644 
1645 inline bool operator >= (const unsigned long int a,const mpreal& b)
1646 {
1647  return mpreal(a)>=b;
1648 }
1649 
1650 inline bool operator >= (const unsigned int a, const mpreal& b)
1651 {
1652  return mpreal(a)>=b;
1653 }
1654 
1655 inline bool operator >= (const long int a, const mpreal& b)
1656 {
1657  return mpreal(a)>=b;
1658 }
1659 
1660 inline bool operator >= (const int a, const mpreal& b)
1661 {
1662  return mpreal(a)>=b;
1663 }
1664 
1665 inline bool operator >= (const long double a, const mpreal& b)
1666 {
1667  return mpreal(a)>=b;
1668 }
1669 
1670 inline bool operator >= (const double a, const mpreal& b)
1671 {
1672  return mpreal(a)>=b;
1673 }
1674 
1675 inline bool operator < (const mpreal& a, const mpreal& b)
1676 {
1677  return (mpfr_less_p(a.mp,b.mp)!=0);
1678 }
1679 
1680 inline bool operator < (const mpreal& a, const unsigned long int b)
1681 {
1682  return a<mpreal(b);
1683 }
1684 
1685 inline bool operator < (const mpreal& a, const unsigned int b)
1686 {
1687  return a<mpreal(b);
1688 }
1689 
1690 inline bool operator < (const mpreal& a, const long int b)
1691 {
1692  return a<mpreal(b);
1693 }
1694 
1695 inline bool operator < (const mpreal& a, const int b)
1696 {
1697  return a<mpreal(b);
1698 }
1699 
1700 inline bool operator < (const mpreal& a, const long double b)
1701 {
1702  return a<mpreal(b);
1703 }
1704 
1705 inline bool operator < (const mpreal& a, const double b)
1706 {
1707  return a<mpreal(b);
1708 }
1709 
1710 inline bool operator < (const unsigned long int a, const mpreal& b)
1711 {
1712  return mpreal(a)<b;
1713 }
1714 
1715 inline bool operator < (const unsigned int a,const mpreal& b)
1716 {
1717  return mpreal(a)<b;
1718 }
1719 
1720 inline bool operator < (const long int a,const mpreal& b)
1721 {
1722  return mpreal(a)<b;
1723 }
1724 
1725 inline bool operator < (const int a,const mpreal& b)
1726 {
1727  return mpreal(a)<b;
1728 }
1729 
1730 inline bool operator < (const long double a,const mpreal& b)
1731 {
1732  return mpreal(a)<b;
1733 }
1734 
1735 inline bool operator < (const double a,const mpreal& b)
1736 {
1737  return mpreal(a)<b;
1738 }
1739 
1740 inline bool operator <= (const mpreal& a, const mpreal& b)
1741 {
1742  return (mpfr_lessequal_p(a.mp,b.mp)!=0);
1743 }
1744 
1745 inline bool operator <= (const mpreal& a, const unsigned long int b)
1746 {
1747  return a<=mpreal(b);
1748 }
1749 
1750 inline bool operator <= (const mpreal& a, const unsigned int b)
1751 {
1752  return a<=mpreal(b);
1753 }
1754 
1755 inline bool operator <= (const mpreal& a, const long int b)
1756 {
1757  return a<=mpreal(b);
1758 }
1759 
1760 inline bool operator <= (const mpreal& a, const int b)
1761 {
1762  return a<=mpreal(b);
1763 }
1764 
1765 inline bool operator <= (const mpreal& a, const long double b)
1766 {
1767  return a<=mpreal(b);
1768 }
1769 
1770 inline bool operator <= (const mpreal& a, const double b)
1771 {
1772  return a<=mpreal(b);
1773 }
1774 
1775 inline bool operator <= (const unsigned long int a,const mpreal& b)
1776 {
1777  return mpreal(a)<=b;
1778 }
1779 
1780 inline bool operator <= (const unsigned int a, const mpreal& b)
1781 {
1782  return mpreal(a)<=b;
1783 }
1784 
1785 inline bool operator <= (const long int a, const mpreal& b)
1786 {
1787  return mpreal(a)<=b;
1788 }
1789 
1790 inline bool operator <= (const int a, const mpreal& b)
1791 {
1792  return mpreal(a)<=b;
1793 }
1794 
1795 inline bool operator <= (const long double a, const mpreal& b)
1796 {
1797  return mpreal(a)<=b;
1798 }
1799 
1800 inline bool operator <= (const double a, const mpreal& b)
1801 {
1802  return mpreal(a)<=b;
1803 }
1804 
1805 inline bool operator == (const mpreal& a, const mpreal& b)
1806 {
1807  return (mpfr_equal_p(a.mp,b.mp)!=0);
1808 }
1809 
1810 inline bool operator == (const mpreal& a, const unsigned long int b)
1811 {
1812  return a==mpreal(b);
1813 }
1814 
1815 inline bool operator == (const mpreal& a, const unsigned int b)
1816 {
1817  return a==mpreal(b);
1818 }
1819 
1820 inline bool operator == (const mpreal& a, const long int b)
1821 {
1822  return a==mpreal(b);
1823 }
1824 
1825 inline bool operator == (const mpreal& a, const int b)
1826 {
1827  return a==mpreal(b);
1828 }
1829 
1830 inline bool operator == (const mpreal& a, const long double b)
1831 {
1832  return a==mpreal(b);
1833 }
1834 
1835 inline bool operator == (const mpreal& a, const double b)
1836 {
1837  return a==mpreal(b);
1838 }
1839 
1840 inline bool operator == (const unsigned long int a,const mpreal& b)
1841 {
1842  return mpreal(a)==b;
1843 }
1844 
1845 inline bool operator == (const unsigned int a, const mpreal& b)
1846 {
1847  return mpreal(a)==b;
1848 }
1849 
1850 inline bool operator == (const long int a, const mpreal& b)
1851 {
1852  return mpreal(a)==b;
1853 }
1854 
1855 inline bool operator == (const int a, const mpreal& b)
1856 {
1857  return mpreal(a)==b;
1858 }
1859 
1860 inline bool operator == (const long double a, const mpreal& b)
1861 {
1862  return mpreal(a)==b;
1863 }
1864 
1865 inline bool operator == (const double a, const mpreal& b)
1866 {
1867  return mpreal(a)==b;
1868 }
1869 
1870 inline bool operator != (const mpreal& a, const mpreal& b)
1871 {
1872  return (mpfr_lessgreater_p(a.mp,b.mp)!=0);
1873 }
1874 
1875 inline bool operator != (const mpreal& a, const unsigned long int b)
1876 {
1877  return a!=mpreal(b);
1878 }
1879 
1880 inline bool operator != (const mpreal& a, const unsigned int b)
1881 {
1882  return a!=mpreal(b);
1883 }
1884 
1885 inline bool operator != (const mpreal& a, const long int b)
1886 {
1887  return a!=mpreal(b);
1888 }
1889 
1890 inline bool operator != (const mpreal& a, const int b)
1891 {
1892  return a!=mpreal(b);
1893 }
1894 
1895 inline bool operator != (const mpreal& a, const long double b)
1896 {
1897  return a!=mpreal(b);
1898 }
1899 
1900 inline bool operator != (const mpreal& a, const double b)
1901 {
1902  return a!=mpreal(b);
1903 }
1904 
1905 inline bool operator != (const unsigned long int a,const mpreal& b)
1906 {
1907  return mpreal(a)!=b;
1908 }
1909 
1910 inline bool operator != (const unsigned int a, const mpreal& b)
1911 {
1912  return mpreal(a)!=b;
1913 }
1914 
1915 inline bool operator != (const long int a, const mpreal& b)
1916 {
1917  return mpreal(a)!=b;
1918 }
1919 
1920 inline bool operator != (const int a, const mpreal& b)
1921 {
1922  return mpreal(a)!=b;
1923 }
1924 
1925 inline bool operator != (const long double a, const mpreal& b)
1926 {
1927  return mpreal(a)!=b;
1928 }
1929 
1930 inline bool operator != (const double a, const mpreal& b)
1931 {
1932  return mpreal(a)!=b;
1933 }
1934 
1935 inline bool _isnan(const mpreal& v)
1936 {
1937  return (mpfr_nan_p(v.mp)!=0);
1938 }
1939 
1940 inline bool _isinf(const mpreal& v)
1941 {
1942  return (mpfr_inf_p(v.mp)!=0);
1943 }
1944 
1945 inline bool _isnum(const mpreal& v)
1946 {
1947  return (mpfr_number_p(v.mp)!=0);
1948 }
1949 
1950 inline bool _iszero(const mpreal& v)
1951 {
1952  return (mpfr_zero_p(v.mp)!=0);
1953 }
1954 
1955 inline bool _isint(const mpreal& v)
1956 {
1957  return (mpfr_integer_p(v.mp)!=0);
1958 }
1959 
1961 // Type Converters
1962 inline mpreal::operator double() const
1963 {
1964  return mpfr_get_d(mp,default_rnd);
1965 }
1966 
1967 inline mpreal::operator float() const
1968 {
1969  return (float)mpfr_get_d(mp,default_rnd);
1970 }
1971 
1972 inline mpreal::operator long double() const
1973 {
1974  return mpfr_get_ld(mp,default_rnd);
1975 }
1976 
1977 inline mpreal::operator unsigned long() const
1978 {
1979  return mpfr_get_ui(mp,default_rnd);
1980 }
1981 
1982 inline mpreal::operator unsigned int() const
1983 {
1984  return mpfr_get_ui(mp,default_rnd);
1985 }
1986 
1987 inline mpreal::operator long() const
1988 {
1989  return mpfr_get_si(mp,default_rnd);
1990 }
1991 
1992 inline mpreal::operator std::string() const
1993 {
1994  return to_string();
1995 }
1996 
1997 inline mpreal::operator mpfr_ptr()
1998 {
1999  return mp;
2000 }
2001 
2003 // Set/Get number properties
2004 inline int sgn(const mpreal& v)
2005 {
2006  int r = mpfr_signbit(v.mp);
2007  return (r>0?-1:1);
2008 }
2009 
2010 inline void mpreal::set_sign(int sign, mp_rnd_t rnd_mode)
2011 {
2012  mpfr_setsign(mp,mp,(sign<0?1:0),rnd_mode);
2013 }
2014 
2015 inline mp_prec_t mpreal::get_prec() const
2016 {
2017  return mpfr_get_prec(mp);
2018 }
2019 
2020 inline void mpreal::set_prec(mp_prec_t prec, mp_rnd_t rnd_mode)
2021 {
2022  mpfr_prec_round(mp,prec,rnd_mode);
2023 }
2024 
2025 inline void mpreal::set_inf(int sign)
2026 {
2027  mpfr_set_inf(mp,sign);
2028 }
2029 
2030 inline void mpreal::set_nan()
2031 {
2032  mpfr_set_nan(mp);
2033 }
2034 
2035 inline mp_exp_t mpreal::get_exp ()
2036 {
2037  return mpfr_get_exp(mp);
2038 }
2039 
2040 inline int mpreal::set_exp (mp_exp_t e)
2041 {
2042  return mpfr_set_exp(mp,e);
2043 }
2044 
2045 inline const mpreal frexp(const mpreal& v, mp_exp_t* exp)
2046 {
2047  mpreal x(v);
2048  *exp = x.get_exp();
2049  x.set_exp(0);
2050  return x;
2051 }
2052 
2053 inline const mpreal ldexp(const mpreal& v, mp_exp_t exp)
2054 {
2055  mpreal x(v);
2056 
2057  // rounding is not important since we just increasing the exponent
2058  mpfr_mul_2si(x.mp,x.mp,exp,mpreal::default_rnd);
2059  return x;
2060 }
2061 
2062 inline const mpreal modf(const mpreal& v, mpreal& n)
2063 {
2064  mpreal frac(v);
2065 
2066  // rounding is not important since we are using the same number
2067  mpfr_frac(frac.mp,frac.mp,mpreal::default_rnd);
2068  mpfr_trunc(n.mp,v.mp);
2069  return frac;
2070 }
2071 
2072 inline int mpreal::check_range (int t, mp_rnd_t rnd_mode)
2073 {
2074  return mpfr_check_range(mp,t,rnd_mode);
2075 }
2076 
2077 inline int mpreal::subnormalize (int t,mp_rnd_t rnd_mode)
2078 {
2079  return mpfr_subnormalize(mp,t,rnd_mode);
2080 }
2081 
2082 inline mp_exp_t mpreal::get_emin (void)
2083 {
2084  return mpfr_get_emin();
2085 }
2086 
2087 inline int mpreal::set_emin (mp_exp_t exp)
2088 {
2089  return mpfr_set_emin(exp);
2090 }
2091 
2092 inline mp_exp_t mpreal::get_emax (void)
2093 {
2094  return mpfr_get_emax();
2095 }
2096 
2097 inline int mpreal::set_emax (mp_exp_t exp)
2098 {
2099  return mpfr_set_emax(exp);
2100 }
2101 
2102 inline mp_exp_t mpreal::get_emin_min (void)
2103 {
2104  return mpfr_get_emin_min();
2105 }
2106 
2107 inline mp_exp_t mpreal::get_emin_max (void)
2108 {
2109  return mpfr_get_emin_max();
2110 }
2111 
2112 inline mp_exp_t mpreal::get_emax_min (void)
2113 {
2114  return mpfr_get_emax_min();
2115 }
2116 
2117 inline mp_exp_t mpreal::get_emax_max (void)
2118 {
2119  return mpfr_get_emax_max();
2120 }
2121 
2123 // Mathematical Functions
2125 inline const mpreal sqr(const mpreal& v, mp_rnd_t rnd_mode)
2126 {
2127  mpreal x(v);
2128  mpfr_sqr(x.mp,x.mp,rnd_mode);
2129  return x;
2130 }
2131 
2132 inline const mpreal sqrt(const mpreal& v, mp_rnd_t rnd_mode)
2133 {
2134  mpreal x(v);
2135  mpfr_sqrt(x.mp,x.mp,rnd_mode);
2136  return x;
2137 }
2138 
2139 inline const mpreal sqrt(const unsigned long int v, mp_rnd_t rnd_mode)
2140 {
2141  mpreal x;
2142  mpfr_sqrt_ui(x.mp,v,rnd_mode);
2143  return x;
2144 }
2145 
2146 inline const mpreal sqrt(const unsigned int v, mp_rnd_t rnd_mode)
2147 {
2148  return sqrt(static_cast<unsigned long int>(v),rnd_mode);
2149 }
2150 
2151 inline const mpreal sqrt(const long int v, mp_rnd_t rnd_mode)
2152 {
2153  if (v>=0) return sqrt(static_cast<unsigned long int>(v),rnd_mode);
2154  else return mpreal(); // NaN
2155 }
2156 
2157 inline const mpreal sqrt(const int v, mp_rnd_t rnd_mode)
2158 {
2159  if (v>=0) return sqrt(static_cast<unsigned long int>(v),rnd_mode);
2160  else return mpreal(); // NaN
2161 }
2162 
2163 inline const mpreal sqrt(const long double v, mp_rnd_t rnd_mode)
2164 {
2165  return sqrt(mpreal(v),rnd_mode);
2166 }
2167 
2168 inline const mpreal sqrt(const double v, mp_rnd_t rnd_mode)
2169 {
2170  return sqrt(mpreal(v),rnd_mode);
2171 }
2172 
2173 inline const mpreal cbrt(const mpreal& v, mp_rnd_t rnd_mode)
2174 {
2175  mpreal x(v);
2176  mpfr_cbrt(x.mp,x.mp,rnd_mode);
2177  return x;
2178 }
2179 
2180 inline const mpreal root(const mpreal& v, unsigned long int k, mp_rnd_t rnd_mode)
2181 {
2182  mpreal x(v);
2183  mpfr_root(x.mp,x.mp,k,rnd_mode);
2184  return x;
2185 }
2186 
2187 inline const mpreal fabs(const mpreal& v, mp_rnd_t rnd_mode)
2188 {
2189  mpreal x(v);
2190  mpfr_abs(x.mp,x.mp,rnd_mode);
2191  return x;
2192 }
2193 
2194 inline const mpreal abs(const mpreal& v, mp_rnd_t rnd_mode)
2195 {
2196  mpreal x(v);
2197  mpfr_abs(x.mp,x.mp,rnd_mode);
2198  return x;
2199 }
2200 
2201 inline const mpreal dim(const mpreal& a, const mpreal& b, mp_rnd_t rnd_mode)
2202 {
2203  mpreal x(a);
2204  mpfr_dim(x.mp,a.mp,b.mp,rnd_mode);
2205  return x;
2206 }
2207 
2208 inline int cmpabs(const mpreal& a,const mpreal& b)
2209 {
2210  return mpfr_cmpabs(a.mp,b.mp);
2211 }
2212 
2213 inline const mpreal log (const mpreal& v, mp_rnd_t rnd_mode)
2214 {
2215  mpreal x(v);
2216  mpfr_log(x.mp,v.mp,rnd_mode);
2217  return x;
2218 }
2219 
2220 inline const mpreal log2(const mpreal& v, mp_rnd_t rnd_mode)
2221 {
2222  mpreal x(v);
2223  mpfr_log2(x.mp,v.mp,rnd_mode);
2224  return x;
2225 }
2226 
2227 inline const mpreal log10(const mpreal& v, mp_rnd_t rnd_mode)
2228 {
2229  mpreal x(v);
2230  mpfr_log10(x.mp,v.mp,rnd_mode);
2231  return x;
2232 }
2233 
2234 inline const mpreal exp(const mpreal& v, mp_rnd_t rnd_mode)
2235 {
2236  mpreal x(v);
2237  mpfr_exp(x.mp,v.mp,rnd_mode);
2238  return x;
2239 }
2240 
2241 inline const mpreal exp2(const mpreal& v, mp_rnd_t rnd_mode)
2242 {
2243  mpreal x(v);
2244  mpfr_exp2(x.mp,v.mp,rnd_mode);
2245  return x;
2246 }
2247 
2248 inline const mpreal exp10(const mpreal& v, mp_rnd_t rnd_mode)
2249 {
2250  mpreal x(v);
2251  mpfr_exp10(x.mp,v.mp,rnd_mode);
2252  return x;
2253 }
2254 
2255 inline const mpreal cos(const mpreal& v, mp_rnd_t rnd_mode)
2256 {
2257  mpreal x(v);
2258  mpfr_cos(x.mp,v.mp,rnd_mode);
2259  return x;
2260 }
2261 
2262 inline const mpreal sin(const mpreal& v, mp_rnd_t rnd_mode)
2263 {
2264  mpreal x(v);
2265  mpfr_sin(x.mp,v.mp,rnd_mode);
2266  return x;
2267 }
2268 
2269 inline const mpreal tan(const mpreal& v, mp_rnd_t rnd_mode)
2270 {
2271  mpreal x(v);
2272  mpfr_tan(x.mp,v.mp,rnd_mode);
2273  return x;
2274 }
2275 
2276 inline const mpreal sec(const mpreal& v, mp_rnd_t rnd_mode)
2277 {
2278  mpreal x(v);
2279  mpfr_sec(x.mp,v.mp,rnd_mode);
2280  return x;
2281 }
2282 
2283 inline const mpreal csc(const mpreal& v, mp_rnd_t rnd_mode)
2284 {
2285  mpreal x(v);
2286  mpfr_csc(x.mp,v.mp,rnd_mode);
2287  return x;
2288 }
2289 
2290 inline const mpreal cot(const mpreal& v, mp_rnd_t rnd_mode)
2291 {
2292  mpreal x(v);
2293  mpfr_cot(x.mp,v.mp,rnd_mode);
2294  return x;
2295 }
2296 
2297 inline int sin_cos(mpreal& s, mpreal& c, const mpreal& v, mp_rnd_t rnd_mode)
2298 {
2299  return mpfr_sin_cos(s.mp,c.mp,v.mp,rnd_mode);
2300 }
2301 
2302 inline const mpreal acos (const mpreal& v, mp_rnd_t rnd_mode)
2303 {
2304  mpreal x(v);
2305  mpfr_acos(x.mp,v.mp,rnd_mode);
2306  return x;
2307 }
2308 
2309 inline const mpreal asin (const mpreal& v, mp_rnd_t rnd_mode)
2310 {
2311  mpreal x(v);
2312  mpfr_asin(x.mp,v.mp,rnd_mode);
2313  return x;
2314 }
2315 
2316 inline const mpreal atan (const mpreal& v, mp_rnd_t rnd_mode)
2317 {
2318  mpreal x(v);
2319  mpfr_atan(x.mp,v.mp,rnd_mode);
2320  return x;
2321 }
2322 
2323 inline const mpreal atan2 (const mpreal& y, const mpreal& x, mp_rnd_t rnd_mode)
2324 {
2325  mpreal a;
2326  mp_prec_t yp, xp;
2327 
2328  yp = y.get_prec();
2329  xp = x.get_prec();
2330 
2331  a.set_prec(yp>xp?yp:xp);
2332 
2333  mpfr_atan2(a.mp, y.mp, x.mp, rnd_mode);
2334 
2335  return a;
2336 }
2337 
2338 inline const mpreal cosh (const mpreal& v, mp_rnd_t rnd_mode)
2339 {
2340  mpreal x(v);
2341  mpfr_cosh(x.mp,v.mp,rnd_mode);
2342  return x;
2343 }
2344 
2345 inline const mpreal sinh (const mpreal& v, mp_rnd_t rnd_mode)
2346 {
2347  mpreal x(v);
2348  mpfr_sinh(x.mp,v.mp,rnd_mode);
2349  return x;
2350 }
2351 
2352 inline const mpreal tanh (const mpreal& v, mp_rnd_t rnd_mode)
2353 {
2354  mpreal x(v);
2355  mpfr_tanh(x.mp,v.mp,rnd_mode);
2356  return x;
2357 }
2358 
2359 inline const mpreal sech (const mpreal& v, mp_rnd_t rnd_mode)
2360 {
2361  mpreal x(v);
2362  mpfr_sech(x.mp,v.mp,rnd_mode);
2363  return x;
2364 }
2365 
2366 inline const mpreal csch (const mpreal& v, mp_rnd_t rnd_mode)
2367 {
2368  mpreal x(v);
2369  mpfr_csch(x.mp,v.mp,rnd_mode);
2370  return x;
2371 }
2372 
2373 inline const mpreal coth (const mpreal& v, mp_rnd_t rnd_mode)
2374 {
2375  mpreal x(v);
2376  mpfr_coth(x.mp,v.mp,rnd_mode);
2377  return x;
2378 }
2379 
2380 inline const mpreal acosh (const mpreal& v, mp_rnd_t rnd_mode)
2381 {
2382  mpreal x(v);
2383  mpfr_acosh(x.mp,v.mp,rnd_mode);
2384  return x;
2385 }
2386 
2387 inline const mpreal asinh (const mpreal& v, mp_rnd_t rnd_mode)
2388 {
2389  mpreal x(v);
2390  mpfr_asinh(x.mp,v.mp,rnd_mode);
2391  return x;
2392 }
2393 
2394 inline const mpreal atanh (const mpreal& v, mp_rnd_t rnd_mode)
2395 {
2396  mpreal x(v);
2397  mpfr_atanh(x.mp,v.mp,rnd_mode);
2398  return x;
2399 }
2400 
2401 inline const mpreal fac_ui (unsigned long int v, mp_rnd_t rnd_mode)
2402 {
2403  mpreal x;
2404  mpfr_fac_ui(x.mp,v,rnd_mode);
2405  return x;
2406 }
2407 
2408 inline const mpreal log1p (const mpreal& v, mp_rnd_t rnd_mode)
2409 {
2410  mpreal x(v);
2411  mpfr_log1p(x.mp,v.mp,rnd_mode);
2412  return x;
2413 }
2414 
2415 inline const mpreal expm1 (const mpreal& v, mp_rnd_t rnd_mode)
2416 {
2417  mpreal x(v);
2418  mpfr_expm1(x.mp,v.mp,rnd_mode);
2419  return x;
2420 }
2421 
2422 inline const mpreal eint (const mpreal& v, mp_rnd_t rnd_mode)
2423 {
2424  mpreal x(v);
2425  mpfr_eint(x.mp,v.mp,rnd_mode);
2426  return x;
2427 }
2428 
2429 inline const mpreal gamma (const mpreal& v, mp_rnd_t rnd_mode)
2430 {
2431  mpreal x(v);
2432  mpfr_gamma(x.mp,v.mp,rnd_mode);
2433  return x;
2434 }
2435 
2436 inline const mpreal lngamma (const mpreal& v, mp_rnd_t rnd_mode)
2437 {
2438  mpreal x(v);
2439  mpfr_lngamma(x.mp,v.mp,rnd_mode);
2440  return x;
2441 }
2442 
2443 inline const mpreal lgamma (const mpreal& v, int *signp, mp_rnd_t rnd_mode)
2444 {
2445  mpreal x(v);
2446  mpfr_lgamma(x.mp,signp,v.mp,rnd_mode);
2447  return x;
2448 }
2449 
2450 inline const mpreal zeta (const mpreal& v, mp_rnd_t rnd_mode)
2451 {
2452  mpreal x(v);
2453  mpfr_zeta(x.mp,v.mp,rnd_mode);
2454  return x;
2455 }
2456 
2457 inline const mpreal erf (const mpreal& v, mp_rnd_t rnd_mode)
2458 {
2459  mpreal x(v);
2460  mpfr_erf(x.mp,v.mp,rnd_mode);
2461  return x;
2462 }
2463 
2464 inline const mpreal erfc (const mpreal& v, mp_rnd_t rnd_mode)
2465 {
2466  mpreal x(v);
2467  mpfr_erfc(x.mp,v.mp,rnd_mode);
2468  return x;
2469 }
2470 
2471 inline const mpreal _j0 (const mpreal& v, mp_rnd_t rnd_mode)
2472 {
2473  mpreal x(v);
2474  mpfr_j0(x.mp,v.mp,rnd_mode);
2475  return x;
2476 }
2477 
2478 inline const mpreal _j1 (const mpreal& v, mp_rnd_t rnd_mode)
2479 {
2480  mpreal x(v);
2481  mpfr_j1(x.mp,v.mp,rnd_mode);
2482  return x;
2483 }
2484 
2485 inline const mpreal _jn (long n, const mpreal& v, mp_rnd_t rnd_mode)
2486 {
2487  mpreal x(v);
2488  mpfr_jn(x.mp,n,v.mp,rnd_mode);
2489  return x;
2490 }
2491 
2492 inline const mpreal _y0 (const mpreal& v, mp_rnd_t rnd_mode)
2493 {
2494  mpreal x(v);
2495  mpfr_y0(x.mp,v.mp,rnd_mode);
2496  return x;
2497 }
2498 
2499 inline const mpreal _y1 (const mpreal& v, mp_rnd_t rnd_mode)
2500 {
2501  mpreal x(v);
2502  mpfr_y1(x.mp,v.mp,rnd_mode);
2503  return x;
2504 }
2505 
2506 inline const mpreal _yn (long n, const mpreal& v, mp_rnd_t rnd_mode)
2507 {
2508  mpreal x(v);
2509  mpfr_yn(x.mp,n,v.mp,rnd_mode);
2510  return x;
2511 }
2512 
2513 
2514 // MPFR 2.4.0 Specifics
2515 #if (MPFR_VERSION >= MPFR_VERSION_NUM(2,4,0))
2516 
2517 inline int sinh_cosh(mpreal& s, mpreal& c, const mpreal& v, mp_rnd_t rnd_mode)
2518 {
2519  return mpfr_sinh_cosh(s.mp,c.mp,v.mp,rnd_mode);
2520 }
2521 
2522 inline const mpreal li2(const mpreal& v, mp_rnd_t rnd_mode)
2523 {
2524  mpreal x(v);
2525  mpfr_li2(x.mp,v.mp,rnd_mode);
2526  return x;
2527 }
2528 
2529 inline const mpreal fmod (const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode)
2530 {
2531  mpreal a;
2532  mp_prec_t yp, xp;
2533 
2534  yp = y.get_prec();
2535  xp = x.get_prec();
2536 
2537  a.set_prec(yp>xp?yp:xp);
2538 
2539  mpfr_fmod(a.mp, x.mp, y.mp, rnd_mode);
2540 
2541  return a;
2542 }
2543 
2544 inline const mpreal rec_sqrt(const mpreal& v, mp_rnd_t rnd_mode)
2545 {
2546  mpreal x(v);
2547  mpfr_rec_sqrt(x.mp,v.mp,rnd_mode);
2548  return x;
2549 }
2550 
2551 #endif
2552 
2554 // Constants
2555 inline const mpreal const_log2 (mp_prec_t prec, mp_rnd_t rnd_mode)
2556 {
2557  mpreal x;
2558  x.set_prec(prec);
2559  mpfr_const_log2(x.mp,rnd_mode);
2560  return x;
2561 }
2562 
2563 inline const mpreal const_pi (mp_prec_t prec, mp_rnd_t rnd_mode)
2564 {
2565  mpreal x;
2566  x.set_prec(prec);
2567  mpfr_const_pi(x.mp,rnd_mode);
2568  return x;
2569 }
2570 
2571 inline const mpreal const_euler (mp_prec_t prec, mp_rnd_t rnd_mode)
2572 {
2573  mpreal x;
2574  x.set_prec(prec);
2575  mpfr_const_euler(x.mp,rnd_mode);
2576  return x;
2577 }
2578 
2579 inline const mpreal const_catalan (mp_prec_t prec, mp_rnd_t rnd_mode)
2580 {
2581  mpreal x;
2582  x.set_prec(prec);
2583  mpfr_const_catalan(x.mp,rnd_mode);
2584  return x;
2585 }
2586 
2588 // Integer Related Functions
2589 inline const mpreal rint(const mpreal& v, mp_rnd_t rnd_mode)
2590 {
2591  mpreal x(v);
2592  mpfr_rint(x.mp,v.mp,rnd_mode);
2593  return x;
2594 }
2595 
2596 inline const mpreal ceil(const mpreal& v)
2597 {
2598  mpreal x(v);
2599  mpfr_ceil(x.mp,v.mp);
2600  return x;
2601 
2602 }
2603 
2604 inline const mpreal floor(const mpreal& v)
2605 {
2606  mpreal x(v);
2607  mpfr_floor(x.mp,v.mp);
2608  return x;
2609 }
2610 
2611 inline const mpreal round(const mpreal& v)
2612 {
2613  mpreal x(v);
2614  mpfr_round(x.mp,v.mp);
2615  return x;
2616 }
2617 
2618 inline const mpreal trunc(const mpreal& v)
2619 {
2620  mpreal x(v);
2621  mpfr_trunc(x.mp,v.mp);
2622  return x;
2623 }
2624 
2625 inline const mpreal rint_ceil (const mpreal& v, mp_rnd_t rnd_mode)
2626 {
2627  mpreal x(v);
2628  mpfr_rint_ceil(x.mp,v.mp,rnd_mode);
2629  return x;
2630 }
2631 
2632 inline const mpreal rint_floor(const mpreal& v, mp_rnd_t rnd_mode)
2633 {
2634  mpreal x(v);
2635  mpfr_rint_floor(x.mp,v.mp,rnd_mode);
2636  return x;
2637 }
2638 
2639 inline const mpreal rint_round(const mpreal& v, mp_rnd_t rnd_mode)
2640 {
2641  mpreal x(v);
2642  mpfr_rint_round(x.mp,v.mp,rnd_mode);
2643  return x;
2644 }
2645 
2646 inline const mpreal rint_trunc(const mpreal& v, mp_rnd_t rnd_mode)
2647 {
2648  mpreal x(v);
2649  mpfr_rint_trunc(x.mp,v.mp,rnd_mode);
2650  return x;
2651 }
2652 
2653 inline const mpreal frac (const mpreal& v, mp_rnd_t rnd_mode)
2654 {
2655  mpreal x(v);
2656  mpfr_frac(x.mp,v.mp,rnd_mode);
2657  return x;
2658 }
2659 
2661 // Miscellaneous Functions
2662 inline void swap(mpreal& a, mpreal& b)
2663 {
2664  mpfr_swap(a.mp,b.mp);
2665 }
2666 
2667 #ifndef max
2668 inline const mpreal max(const mpreal& x, const mpreal& y)
2669 {
2670  return (x>y?x:y);
2671 }
2672 #endif
2673 
2674 #ifndef min
2675 inline const mpreal min(const mpreal& x, const mpreal& y)
2676 {
2677  return (x<y?x:y);
2678 }
2679 #endif
2680 
2681 inline const mpreal nexttoward (const mpreal& x, const mpreal& y)
2682 {
2683  mpreal a(x);
2684  mpfr_nexttoward(a.mp,y.mp);
2685  return a;
2686 }
2687 
2688 inline const mpreal nextabove (const mpreal& x)
2689 {
2690  mpreal a(x);
2691  mpfr_nextabove(a.mp);
2692  return a;
2693 }
2694 
2695 inline const mpreal nextbelow (const mpreal& x)
2696 {
2697  mpreal a(x);
2698  mpfr_nextbelow(a.mp);
2699  return a;
2700 }
2701 
2702 inline const mpreal urandomb (gmp_randstate_t& state)
2703 {
2704  mpreal x;
2705  mpfr_urandomb(x.mp,state);
2706  return x;
2707 }
2708 
2709 // inline const mpreal random2 (mp_size_t size, mp_exp_t exp)
2710 // {
2711 // mpreal x;
2712 // mpfr_random2(x.mp,size,exp);
2713 // return x;
2714 // }
2715 
2717 // Set/Get global properties
2718 inline void mpreal::set_default_prec(mp_prec_t prec)
2719 {
2720  default_prec = prec;
2721  mpfr_set_default_prec(prec);
2722 }
2723 
2724 inline mp_prec_t mpreal::get_default_prec()
2725 {
2726  return mpfr_get_default_prec();
2727 }
2728 
2729 inline void mpreal::set_default_base(int base)
2730 {
2731  default_base = base;
2732 }
2733 
2734 inline int mpreal::get_default_base()
2735 {
2736  return default_base;
2737 }
2738 
2739 inline void mpreal::set_default_rnd(mp_rnd_t rnd_mode)
2740 {
2741  default_rnd = rnd_mode;
2742  mpfr_set_default_rounding_mode(rnd_mode);
2743 }
2744 
2745 inline mp_rnd_t mpreal::get_default_rnd()
2746 {
2747  return mpfr_get_default_rounding_mode();
2748 }
2749 
2750 inline void mpreal::set_double_bits(int dbits)
2751 {
2752  double_bits = dbits;
2753 }
2754 
2755 inline int mpreal::get_double_bits()
2756 {
2757  return double_bits;
2758 }
2759 
2760 inline bool mpreal::fits_in_bits(double x, int n)
2761 {
2762  int i;
2763  double t;
2764  return IsInf(x) || (std::modf ( std::ldexp ( std::frexp ( x, &i ), n ), &t ) == 0.0);
2765 }
2766 
2767 inline const mpreal pow(const mpreal& a, const mpreal& b, mp_rnd_t rnd_mode)
2768 {
2769  mpreal x(a);
2770  mpfr_pow(x.mp,x.mp,b.mp,rnd_mode);
2771  return x;
2772 }
2773 
2774 inline const mpreal pow(const mpreal& a, const mpz_t b, mp_rnd_t rnd_mode)
2775 {
2776  mpreal x(a);
2777  mpfr_pow_z(x.mp,x.mp,b,rnd_mode);
2778  return x;
2779 }
2780 
2781 inline const mpreal pow(const mpreal& a, const unsigned long int b, mp_rnd_t rnd_mode)
2782 {
2783  mpreal x(a);
2784  mpfr_pow_ui(x.mp,x.mp,b,rnd_mode);
2785  return x;
2786 }
2787 
2788 inline const mpreal pow(const mpreal& a, const unsigned int b, mp_rnd_t rnd_mode)
2789 {
2790  return pow(a,static_cast<unsigned long int>(b),rnd_mode);
2791 }
2792 
2793 inline const mpreal pow(const mpreal& a, const long int b, mp_rnd_t rnd_mode)
2794 {
2795  mpreal x(a);
2796  mpfr_pow_si(x.mp,x.mp,b,rnd_mode);
2797  return x;
2798 }
2799 
2800 inline const mpreal pow(const mpreal& a, const int b, mp_rnd_t rnd_mode)
2801 {
2802  return pow(a,static_cast<long int>(b),rnd_mode);
2803 }
2804 
2805 inline const mpreal pow(const mpreal& a, const long double b, mp_rnd_t rnd_mode)
2806 {
2807  return pow(a,mpreal(b),rnd_mode);
2808 }
2809 
2810 inline const mpreal pow(const mpreal& a, const double b, mp_rnd_t rnd_mode)
2811 {
2812  return pow(a,mpreal(b),rnd_mode);
2813 }
2814 
2815 inline const mpreal pow(const unsigned long int a, const mpreal& b, mp_rnd_t rnd_mode)
2816 {
2817  mpreal x(a);
2818  mpfr_ui_pow(x.mp,a,b.mp,rnd_mode);
2819  return x;
2820 }
2821 
2822 inline const mpreal pow(const unsigned int a, const mpreal& b, mp_rnd_t rnd_mode)
2823 {
2824  return pow(static_cast<unsigned long int>(a),b,rnd_mode);
2825 }
2826 
2827 inline const mpreal pow(const long int a, const mpreal& b, mp_rnd_t rnd_mode)
2828 {
2829  if (a>=0) return pow(static_cast<unsigned long int>(a),b,rnd_mode);
2830  else return pow(mpreal(a),b,rnd_mode);
2831 }
2832 
2833 inline const mpreal pow(const int a, const mpreal& b, mp_rnd_t rnd_mode)
2834 {
2835  if (a>=0) return pow(static_cast<unsigned long int>(a),b,rnd_mode);
2836  else return pow(mpreal(a),b,rnd_mode);
2837 }
2838 
2839 inline const mpreal pow(const long double a, const mpreal& b, mp_rnd_t rnd_mode)
2840 {
2841  return pow(mpreal(a),b,rnd_mode);
2842 }
2843 
2844 inline const mpreal pow(const double a, const mpreal& b, mp_rnd_t rnd_mode)
2845 {
2846  return pow(mpreal(a),b,rnd_mode);
2847 }
2848 
2849 // pow unsigned long int
2850 inline const mpreal pow(const unsigned long int a, const unsigned long int b, mp_rnd_t rnd_mode)
2851 {
2852  mpreal x(a);
2853  mpfr_ui_pow_ui(x.mp,a,b,rnd_mode);
2854  return x;
2855 }
2856 
2857 inline const mpreal pow(const unsigned long int a, const unsigned int b, mp_rnd_t rnd_mode)
2858 {
2859  return pow(a,static_cast<unsigned long int>(b),rnd_mode); //mpfr_ui_pow_ui
2860 }
2861 
2862 inline const mpreal pow(const unsigned long int a, const long int b, mp_rnd_t rnd_mode)
2863 {
2864  if(b>0) return pow(a,static_cast<unsigned long int>(b),rnd_mode); //mpfr_ui_pow_ui
2865  else return pow(a,mpreal(b),rnd_mode); //mpfr_ui_pow
2866 }
2867 
2868 inline const mpreal pow(const unsigned long int a, const int b, mp_rnd_t rnd_mode)
2869 {
2870  if(b>0) return pow(a,static_cast<unsigned long int>(b),rnd_mode); //mpfr_ui_pow_ui
2871  else return pow(a,mpreal(b),rnd_mode); //mpfr_ui_pow
2872 }
2873 
2874 inline const mpreal pow(const unsigned long int a, const long double b, mp_rnd_t rnd_mode)
2875 {
2876  return pow(a,mpreal(b),rnd_mode); //mpfr_ui_pow
2877 }
2878 
2879 inline const mpreal pow(const unsigned long int a, const double b, mp_rnd_t rnd_mode)
2880 {
2881  return pow(a,mpreal(b),rnd_mode); //mpfr_ui_pow
2882 }
2883 
2884 // pow unsigned int
2885 inline const mpreal pow(const unsigned int a, const unsigned long int b, mp_rnd_t rnd_mode)
2886 {
2887  return pow(static_cast<unsigned long int>(a),b,rnd_mode); //mpfr_ui_pow_ui
2888 }
2889 
2890 inline const mpreal pow(const unsigned int a, const unsigned int b, mp_rnd_t rnd_mode)
2891 {
2892  return pow(static_cast<unsigned long int>(a),static_cast<unsigned long int>(b),rnd_mode); //mpfr_ui_pow_ui
2893 }
2894 
2895 inline const mpreal pow(const unsigned int a, const long int b, mp_rnd_t rnd_mode)
2896 {
2897  if(b>0) return pow(static_cast<unsigned long int>(a),static_cast<unsigned long int>(b),rnd_mode); //mpfr_ui_pow_ui
2898  else return pow(static_cast<unsigned long int>(a),mpreal(b),rnd_mode); //mpfr_ui_pow
2899 }
2900 
2901 inline const mpreal pow(const unsigned int a, const int b, mp_rnd_t rnd_mode)
2902 {
2903  if(b>0) return pow(static_cast<unsigned long int>(a),static_cast<unsigned long int>(b),rnd_mode); //mpfr_ui_pow_ui
2904  else return pow(static_cast<unsigned long int>(a),mpreal(b),rnd_mode); //mpfr_ui_pow
2905 }
2906 
2907 inline const mpreal pow(const unsigned int a, const long double b, mp_rnd_t rnd_mode)
2908 {
2909  return pow(static_cast<unsigned long int>(a),mpreal(b),rnd_mode); //mpfr_ui_pow
2910 }
2911 
2912 inline const mpreal pow(const unsigned int a, const double b, mp_rnd_t rnd_mode)
2913 {
2914  return pow(static_cast<unsigned long int>(a),mpreal(b),rnd_mode); //mpfr_ui_pow
2915 }
2916 
2917 // pow long int
2918 inline const mpreal pow(const long int a, const unsigned long int b, mp_rnd_t rnd_mode)
2919 {
2920  if (a>0) return pow(static_cast<unsigned long int>(a),b,rnd_mode); //mpfr_ui_pow_ui
2921  else return pow(mpreal(a),b,rnd_mode); //mpfr_pow_ui
2922 }
2923 
2924 inline const mpreal pow(const long int a, const unsigned int b, mp_rnd_t rnd_mode)
2925 {
2926  if (a>0) return pow(static_cast<unsigned long int>(a),static_cast<unsigned long int>(b),rnd_mode); //mpfr_ui_pow_ui
2927  else return pow(mpreal(a),static_cast<unsigned long int>(b),rnd_mode); //mpfr_pow_ui
2928 }
2929 
2930 inline const mpreal pow(const long int a, const long int b, mp_rnd_t rnd_mode)
2931 {
2932  if (a>0)
2933  {
2934  if(b>0) return pow(static_cast<unsigned long int>(a),static_cast<unsigned long int>(b),rnd_mode); //mpfr_ui_pow_ui
2935  else return pow(static_cast<unsigned long int>(a),mpreal(b),rnd_mode); //mpfr_ui_pow
2936  }else{
2937  return pow(mpreal(a),b,rnd_mode); // mpfr_pow_si
2938  }
2939 }
2940 
2941 inline const mpreal pow(const long int a, const int b, mp_rnd_t rnd_mode)
2942 {
2943  if (a>0)
2944  {
2945  if(b>0) return pow(static_cast<unsigned long int>(a),static_cast<unsigned long int>(b),rnd_mode); //mpfr_ui_pow_ui
2946  else return pow(static_cast<unsigned long int>(a),mpreal(b),rnd_mode); //mpfr_ui_pow
2947  }else{
2948  return pow(mpreal(a),static_cast<long int>(b),rnd_mode); // mpfr_pow_si
2949  }
2950 }
2951 
2952 inline const mpreal pow(const long int a, const long double b, mp_rnd_t rnd_mode)
2953 {
2954  if (a>=0) return pow(static_cast<unsigned long int>(a),mpreal(b),rnd_mode); //mpfr_ui_pow
2955  else return pow(mpreal(a),mpreal(b),rnd_mode); //mpfr_pow
2956 }
2957 
2958 inline const mpreal pow(const long int a, const double b, mp_rnd_t rnd_mode)
2959 {
2960  if (a>=0) return pow(static_cast<unsigned long int>(a),mpreal(b),rnd_mode); //mpfr_ui_pow
2961  else return pow(mpreal(a),mpreal(b),rnd_mode); //mpfr_pow
2962 }
2963 
2964 // pow int
2965 inline const mpreal pow(const int a, const unsigned long int b, mp_rnd_t rnd_mode)
2966 {
2967  if (a>0) return pow(static_cast<unsigned long int>(a),b,rnd_mode); //mpfr_ui_pow_ui
2968  else return pow(mpreal(a),b,rnd_mode); //mpfr_pow_ui
2969 }
2970 
2971 inline const mpreal pow(const int a, const unsigned int b, mp_rnd_t rnd_mode)
2972 {
2973  if (a>0) return pow(static_cast<unsigned long int>(a),static_cast<unsigned long int>(b),rnd_mode); //mpfr_ui_pow_ui
2974  else return pow(mpreal(a),static_cast<unsigned long int>(b),rnd_mode); //mpfr_pow_ui
2975 }
2976 
2977 inline const mpreal pow(const int a, const long int b, mp_rnd_t rnd_mode)
2978 {
2979  if (a>0)
2980  {
2981  if(b>0) return pow(static_cast<unsigned long int>(a),static_cast<unsigned long int>(b),rnd_mode); //mpfr_ui_pow_ui
2982  else return pow(static_cast<unsigned long int>(a),mpreal(b),rnd_mode); //mpfr_ui_pow
2983  }else{
2984  return pow(mpreal(a),b,rnd_mode); // mpfr_pow_si
2985  }
2986 }
2987 
2988 inline const mpreal pow(const int a, const int b, mp_rnd_t rnd_mode)
2989 {
2990  if (a>0)
2991  {
2992  if(b>0) return pow(static_cast<unsigned long int>(a),static_cast<unsigned long int>(b),rnd_mode); //mpfr_ui_pow_ui
2993  else return pow(static_cast<unsigned long int>(a),mpreal(b),rnd_mode); //mpfr_ui_pow
2994  }else{
2995  return pow(mpreal(a),static_cast<long int>(b),rnd_mode); // mpfr_pow_si
2996  }
2997 }
2998 
2999 inline const mpreal pow(const int a, const long double b, mp_rnd_t rnd_mode)
3000 {
3001  if (a>=0) return pow(static_cast<unsigned long int>(a),mpreal(b),rnd_mode); //mpfr_ui_pow
3002  else return pow(mpreal(a),mpreal(b),rnd_mode); //mpfr_pow
3003 }
3004 
3005 inline const mpreal pow(const int a, const double b, mp_rnd_t rnd_mode)
3006 {
3007  if (a>=0) return pow(static_cast<unsigned long int>(a),mpreal(b),rnd_mode); //mpfr_ui_pow
3008  else return pow(mpreal(a),mpreal(b),rnd_mode); //mpfr_pow
3009 }
3010 
3011 // pow long double
3012 inline const mpreal pow(const long double a, const long double b, mp_rnd_t rnd_mode)
3013 {
3014  return pow(mpreal(a),mpreal(b),rnd_mode);
3015 }
3016 
3017 inline const mpreal pow(const long double a, const unsigned long int b, mp_rnd_t rnd_mode)
3018 {
3019  return pow(mpreal(a),b,rnd_mode); //mpfr_pow_ui
3020 }
3021 
3022 inline const mpreal pow(const long double a, const unsigned int b, mp_rnd_t rnd_mode)
3023 {
3024  return pow(mpreal(a),static_cast<unsigned long int>(b),rnd_mode); //mpfr_pow_ui
3025 }
3026 
3027 inline const mpreal pow(const long double a, const long int b, mp_rnd_t rnd_mode)
3028 {
3029  return pow(mpreal(a),b,rnd_mode); // mpfr_pow_si
3030 }
3031 
3032 inline const mpreal pow(const long double a, const int b, mp_rnd_t rnd_mode)
3033 {
3034  return pow(mpreal(a),static_cast<long int>(b),rnd_mode); // mpfr_pow_si
3035 }
3036 
3037 inline const mpreal pow(const double a, const double b, mp_rnd_t rnd_mode)
3038 {
3039  return pow(mpreal(a),mpreal(b),rnd_mode);
3040 }
3041 
3042 inline const mpreal pow(const double a, const unsigned long int b, mp_rnd_t rnd_mode)
3043 {
3044  return pow(mpreal(a),b,rnd_mode); // mpfr_pow_ui
3045 }
3046 
3047 inline const mpreal pow(const double a, const unsigned int b, mp_rnd_t rnd_mode)
3048 {
3049  return pow(mpreal(a),static_cast<unsigned long int>(b),rnd_mode); // mpfr_pow_ui
3050 }
3051 
3052 inline const mpreal pow(const double a, const long int b, mp_rnd_t rnd_mode)
3053 {
3054  return pow(mpreal(a),b,rnd_mode); // mpfr_pow_si
3055 }
3056 
3057 inline const mpreal pow(const double a, const int b, mp_rnd_t rnd_mode)
3058 {
3059  return pow(mpreal(a),static_cast<long int>(b),rnd_mode); // mpfr_pow_si
3060 }
3061 }
3062 
3063 // Explicit specialization of std::swap for mpreal numbers
3064 // Thus standard algorithms will use efficient version of swap (due to Koenig lookup)
3065 // Non-throwing swap C++ idiom: http://en.wikibooks.org/wiki/More_C%2B%2B_Idioms/Non-throwing_swap
3066 namespace std
3067 {
3068  template <>
3069  inline void swap(mpfr::mpreal& x, mpfr::mpreal& y)
3070  {
3071  return mpfr::swap(x, y);
3072  }
3073 }
3074 
3075 #endif /* __MP_REAL_H__ */
mpfr::mpreal::fma
friend const mpreal fma(const mpreal &v1, const mpreal &v2, const mpreal &v3, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.cc:181
mpfr::mpreal::acosh
friend const mpreal acosh(const mpreal &v, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.h:2380
mpfr::mpreal::nexttoward
friend const mpreal nexttoward(const mpreal &x, const mpreal &y)
Definition: mpreal.h:2681
mpfr::exp2
const mpreal exp2(const mpreal &v, mp_rnd_t rnd_mode)
Definition: mpreal.h:2241
mpfr::mpreal::get_exp
mp_exp_t get_exp()
Definition: mpreal.h:2035
mpfr::mpreal::const_pi
friend const mpreal const_pi(mp_prec_t prec=mpreal::default_prec, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.h:2563
mpfr::mpreal::atan2
friend const mpreal atan2(const mpreal &y, const mpreal &x, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.h:2323
mpfr::mpreal::operator!=
friend bool operator!=(const mpreal &a, const mpreal &b)
Definition: mpreal.h:1870
mpfr::operator<
bool operator<(const mpreal &a, const unsigned long int b)
Definition: mpreal.h:1680
mpfr::mpreal::default_base
static int default_base
Definition: mpreal.h:92
mpfr::mpreal::operator>>
friend std::istream & operator>>(std::istream &is, mpreal &v)
mpfr::mpreal::frexp
friend const mpreal frexp(const mpreal &v, mp_exp_t *exp)
Definition: mpreal.h:2045
mpfr::erfc
const mpreal erfc(const mpreal &v, mp_rnd_t rnd_mode)
Definition: mpreal.h:2464
mpfr::exp
const mpreal exp(const mpreal &v, mp_rnd_t rnd_mode)
Definition: mpreal.h:2234
mpfr::mpreal::get_default_base
static int get_default_base()
Definition: mpreal.h:2734
mpfr::_jn
const mpreal _jn(long n, const mpreal &v, mp_rnd_t rnd_mode)
Definition: mpreal.h:2485
mpfr::mpreal::modf
friend const mpreal modf(const mpreal &v, mpreal &n)
Definition: mpreal.h:2062
mpfr::sqr
const mpreal sqr(const mpreal &v, mp_rnd_t rnd_mode)
Definition: mpreal.h:2125
mpfr::operator<<
ostream & operator<<(ostream &os, const mpreal &v)
Definition: mpreal.cc:391
mpfr::erf
const mpreal erf(const mpreal &v, mp_rnd_t rnd_mode)
Definition: mpreal.h:2457
mpfr::exp10
const mpreal exp10(const mpreal &v, mp_rnd_t rnd_mode)
Definition: mpreal.h:2248
mpfr::_isnan
bool _isnan(const mpreal &v)
Definition: mpreal.h:1935
mpfr::mpreal::urandomb
friend const mpreal urandomb(gmp_randstate_t &state)
Definition: mpreal.h:2702
mpfr::mpreal::operator<=
friend bool operator<=(const mpreal &a, const mpreal &b)
Definition: mpreal.h:1740
mpfr::mpreal::set_emax
static int set_emax(mp_exp_t exp)
Definition: mpreal.h:2097
mpfr::mpreal::subnormalize
int subnormalize(int t, mp_rnd_t rnd_mode=default_rnd)
Definition: mpreal.h:2077
mpfr::mpreal::operator/
friend const mpreal operator/(const unsigned long int b, const mpreal &a)
Definition: mpreal.h:1377
mpfr::cmpabs
int cmpabs(const mpreal &a, const mpreal &b)
Definition: mpreal.h:2208
mpfr::log
const mpreal log(const mpreal &v, mp_rnd_t rnd_mode)
Definition: mpreal.h:2213
mpfr::mpreal::sgn
friend int sgn(const mpreal &v)
Definition: mpreal.h:2004
mpfr::mpreal::operator/=
mpreal & operator/=(const mpreal &v)
Definition: mpreal.h:1266
mpfr::cosh
const mpreal cosh(const mpreal &v, mp_rnd_t rnd_mode)
Definition: mpreal.h:2338
mpfr::mpreal::default_prec
static mp_prec_t default_prec
Definition: mpreal.h:91
mpfr::mpreal::root
friend const mpreal root(const mpreal &v, unsigned long int k, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.h:2180
mpfr::mpreal::tanh
friend const mpreal tanh(const mpreal &v, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.h:2352
mpfr::sec
const mpreal sec(const mpreal &v, mp_rnd_t rnd_mode)
Definition: mpreal.h:2276
mpfr::mpreal::abs
friend const mpreal abs(const mpreal &v, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.h:2194
mpfr::mpreal::agm
friend const mpreal agm(const mpreal &v1, const mpreal &v2, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.cc:211
mpfr::_y1
const mpreal _y1(const mpreal &v, mp_rnd_t rnd_mode)
Definition: mpreal.h:2499
mpfr::abs
const mpreal abs(const mpreal &v, mp_rnd_t rnd_mode)
Definition: mpreal.h:2194
mpfr::mpreal::acos
friend const mpreal acos(const mpreal &v, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.h:2302
mpfr::fac_ui
const mpreal fac_ui(unsigned long int v, mp_rnd_t rnd_mode)
Definition: mpreal.h:2401
mpfr::nexttoward
const mpreal nexttoward(const mpreal &x, const mpreal &y)
Definition: mpreal.h:2681
mpfr::mpreal::fms
friend const mpreal fms(const mpreal &v1, const mpreal &v2, const mpreal &v3, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.cc:196
mpfr::mpreal::_iszero
friend bool _iszero(const mpreal &v)
Definition: mpreal.h:1950
mpfr::pow
const mpreal pow(const mpreal &a, const unsigned int b, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.h:2788
mpfr::mpreal
Definition: mpreal.h:85
mpfr::mpreal::get_prec
mp_prec_t get_prec() const
Definition: mpreal.h:2015
mpfr::mpreal::sum
friend const mpreal sum(const mpreal tab[], unsigned long int n, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.cc:241
mpfr::mpreal::_y1
friend const mpreal _y1(const mpreal &v, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.h:2499
mpfr::acosh
const mpreal acosh(const mpreal &v, mp_rnd_t rnd_mode)
Definition: mpreal.h:2380
mpfr::mpreal::cmpabs
friend int cmpabs(const mpreal &a, const mpreal &b)
Definition: mpreal.h:2208
mpfr::operator!=
bool operator!=(const mpreal &a, const unsigned long int b)
Definition: mpreal.h:1875
mpfr::mpreal::_isint
friend bool _isint(const mpreal &v)
Definition: mpreal.h:1955
mpfr::mpreal::operator>>=
mpreal & operator>>=(const unsigned long int u)
Definition: mpreal.h:1449
mpfr::mpreal::coth
friend const mpreal coth(const mpreal &v, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.h:2373
mpfr::dim
const mpreal dim(const mpreal &a, const mpreal &b, mp_rnd_t rnd_mode)
Definition: mpreal.h:2201
mpfr::frac
const mpreal frac(const mpreal &v, mp_rnd_t rnd_mode)
Definition: mpreal.h:2653
mpfr::_isint
bool _isint(const mpreal &v)
Definition: mpreal.h:1955
mpfr::ldexp
const mpreal ldexp(const mpreal &v, mp_exp_t exp)
Definition: mpreal.h:2053
mpfr::mpreal::mpreal
mpreal()
Definition: mpreal.cc:77
mpfr::mpreal::hypot
friend const mpreal hypot(const mpreal &x, const mpreal &y, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.cc:226
mpfr::max
const mpreal max(const mpreal &x, const mpreal &y)
Definition: mpreal.h:2668
testing::internal::string
::std::string string
Definition: gtest-port.h:872
mpfr::fmod
const mpreal fmod(const mpreal &x, const mpreal &y, mp_rnd_t rnd_mode)
Definition: mpreal.h:2529
mpfr::mpreal::asinh
friend const mpreal asinh(const mpreal &v, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.h:2387
mpfr::const_euler
const mpreal const_euler(mp_prec_t prec, mp_rnd_t rnd_mode)
Definition: mpreal.h:2571
mpfr::mpreal::_j1
friend const mpreal _j1(const mpreal &v, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.h:2478
mpfr::mpreal::double_bits
static int double_bits
Definition: mpreal.h:93
mpfr::cbrt
const mpreal cbrt(const mpreal &v, mp_rnd_t rnd_mode)
Definition: mpreal.h:2173
mpfr::mpreal::set_prec
void set_prec(mp_prec_t prec, mp_rnd_t rnd_mode=default_rnd)
Definition: mpreal.h:2020
mpfr::cos
const mpreal cos(const mpreal &v, mp_rnd_t rnd_mode)
Definition: mpreal.h:2255
mpfr::mpreal::zeta
friend const mpreal zeta(const mpreal &v, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.h:2450
mpfr::mul_2si
const mpreal mul_2si(const mpreal &v, long int k, mp_rnd_t rnd_mode)
Definition: mpreal.h:1522
mpfr::rint
const mpreal rint(const mpreal &v, mp_rnd_t rnd_mode)
Definition: mpreal.h:2589
mpfr::mpreal::get_emin
static mp_exp_t get_emin(void)
Definition: mpreal.h:2082
std
Definition: mpreal.h:3066
mpfr::mpreal::sin
friend const mpreal sin(const mpreal &v, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.h:2262
mpfr::conversion_overflow
Definition: mpreal.h:415
mpfr
Definition: mpreal.cc:69
mpfr::mpreal::random2
friend const mpreal random2(mp_size_t size, mp_exp_t exp)
mpfr::mpreal::fac_ui
friend const mpreal fac_ui(unsigned long int v, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.h:2401
mpfr::operator>
bool operator>(const mpreal &a, const unsigned long int b)
Definition: mpreal.h:1550
mpfr::conversion_overflow::why
std::string why()
Definition: mpreal.h:417
mpfr::mpreal::get_default_rnd
static mp_rnd_t get_default_rnd()
Definition: mpreal.h:2745
mpfr::mpreal::li2
friend const mpreal li2(const mpreal &v, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.h:2522
mpfr::operator==
bool operator==(const mpreal &a, const unsigned long int b)
Definition: mpreal.h:1810
mpfr::mpreal::get_double_bits
static int get_double_bits()
Definition: mpreal.h:2755
mpfr::sinh_cosh
int sinh_cosh(mpreal &s, mpreal &c, const mpreal &v, mp_rnd_t rnd_mode)
Definition: mpreal.h:2517
mpfr::mpreal::operator--
mpreal & operator--()
Definition: mpreal.h:928
mpfr::mpreal::nextabove
friend const mpreal nextabove(const mpreal &x)
Definition: mpreal.h:2688
mpfr::mpreal::mul_2ui
friend const mpreal mul_2ui(const mpreal &v, unsigned long int k, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.h:1514
mpfr::cot
const mpreal cot(const mpreal &v, mp_rnd_t rnd_mode)
Definition: mpreal.h:2290
IsInf
#define IsInf(x)
Definition: mpreal.h:80
mpfr::mpreal::cos
friend const mpreal cos(const mpreal &v, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.h:2255
mpfr::mpreal::operator*=
mpreal & operator*=(const mpreal &v)
Definition: mpreal.h:1120
mpfr::mpreal::expm1
friend const mpreal expm1(const mpreal &v, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.h:2415
mpfr::sgn
int sgn(const mpreal &v)
Definition: mpreal.h:2004
mpfr::rint_round
const mpreal rint_round(const mpreal &v, mp_rnd_t rnd_mode)
Definition: mpreal.h:2639
mpfr::operator*
const mpreal operator*(const mpreal &a, const mpreal &b)
Definition: mpreal.h:1177
mpfr::ceil
const mpreal ceil(const mpreal &v)
Definition: mpreal.h:2596
mpfr::mpreal::sqrt
friend const mpreal sqrt(const mpreal &v, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.h:2132
mpfr::asinh
const mpreal asinh(const mpreal &v, mp_rnd_t rnd_mode)
Definition: mpreal.h:2387
mpfr::swap
void swap(mpreal &a, mpreal &b)
Definition: mpreal.h:2662
mpfr::mpreal::lgamma
friend const mpreal lgamma(const mpreal &v, int *signp, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.h:2443
mpfr::mpreal::div_2ui
friend const mpreal div_2ui(const mpreal &v, unsigned long int k, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.h:1529
mpfr::mpreal::sin_cos
friend int sin_cos(mpreal &s, mpreal &c, const mpreal &v, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.h:2297
mpfr::mpreal::swap
friend void swap(mpreal &x, mpreal &y)
Definition: mpreal.h:2662
mpfr::_yn
const mpreal _yn(long n, const mpreal &v, mp_rnd_t rnd_mode)
Definition: mpreal.h:2506
mpfr::mpreal::get_emin_min
static mp_exp_t get_emin_min(void)
Definition: mpreal.h:2102
mpfr::mpreal::cot
friend const mpreal cot(const mpreal &v, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.h:2290
mpfr::mpreal::remainder
friend const mpreal remainder(const mpreal &x, const mpreal &y, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.cc:254
mpfr::mpreal::operator>
friend bool operator>(const mpreal &a, const mpreal &b)
Definition: mpreal.h:1545
mpfr::modf
const mpreal modf(const mpreal &v, mpreal &n)
Definition: mpreal.h:2062
mpfr::atan2
const mpreal atan2(const mpreal &y, const mpreal &x, mp_rnd_t rnd_mode)
Definition: mpreal.h:2323
mpfr::mpreal::get_emax
static mp_exp_t get_emax(void)
Definition: mpreal.h:2092
mpfr::mpreal::operator-
const mpreal operator-() const
Definition: mpreal.h:1000
mpfr::mpreal::exp
friend const mpreal exp(const mpreal &v, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.h:2234
mpfr::_j0
const mpreal _j0(const mpreal &v, mp_rnd_t rnd_mode)
Definition: mpreal.h:2471
mpfr::operator<=
bool operator<=(const mpreal &a, const unsigned long int b)
Definition: mpreal.h:1745
mpfr::acos
const mpreal acos(const mpreal &v, mp_rnd_t rnd_mode)
Definition: mpreal.h:2302
mpfr::eint
const mpreal eint(const mpreal &v, mp_rnd_t rnd_mode)
Definition: mpreal.h:2422
mpfr::mpreal::_isnan
friend bool _isnan(const mpreal &v)
Definition: mpreal.h:1935
mpfr::mpreal::operator==
friend bool operator==(const mpreal &a, const mpreal &b)
Definition: mpreal.h:1805
mpfr::rec_sqrt
const mpreal rec_sqrt(const mpreal &v, mp_rnd_t rnd_mode)
Definition: mpreal.h:2544
mpfr::mpreal::get_emax_max
static mp_exp_t get_emax_max(void)
Definition: mpreal.h:2117
mpfr::operator>>
istream & operator>>(istream &is, mpreal &v)
Definition: mpreal.cc:396
mpfr::rint_trunc
const mpreal rint_trunc(const mpreal &v, mp_rnd_t rnd_mode)
Definition: mpreal.h:2646
mpfr::mpreal::cbrt
friend const mpreal cbrt(const mpreal &v, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.h:2173
mpfr::mpreal::mul_2si
friend const mpreal mul_2si(const mpreal &v, long int k, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.h:1522
mpfr::mpreal::rint_trunc
friend const mpreal rint_trunc(const mpreal &v, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.h:2646
mpfr::lngamma
const mpreal lngamma(const mpreal &v, mp_rnd_t rnd_mode)
Definition: mpreal.h:2436
mpfr::_j1
const mpreal _j1(const mpreal &v, mp_rnd_t rnd_mode)
Definition: mpreal.h:2478
mpfr::mpreal::floor
friend const mpreal floor(const mpreal &v)
Definition: mpreal.h:2604
mpfr::mpreal::max
friend const mpreal max(const mpreal &x, const mpreal &y)
Definition: mpreal.h:2668
mpfr::log2
const mpreal log2(const mpreal &v, mp_rnd_t rnd_mode)
Definition: mpreal.h:2220
mpfr::mpreal::set_nan
void set_nan()
Definition: mpreal.h:2030
mpfr::mpreal::set_default_base
static void set_default_base(int base)
Definition: mpreal.h:2729
mpfr::rint_floor
const mpreal rint_floor(const mpreal &v, mp_rnd_t rnd_mode)
Definition: mpreal.h:2632
mpfr::log10
const mpreal log10(const mpreal &v, mp_rnd_t rnd_mode)
Definition: mpreal.h:2227
mpfr::min
const mpreal min(const mpreal &x, const mpreal &y)
Definition: mpreal.h:2675
mpfr::rint_ceil
const mpreal rint_ceil(const mpreal &v, mp_rnd_t rnd_mode)
Definition: mpreal.h:2625
a
FLOAT a(int j, FLOAT z)
Definition: y1.cc:86
mpfr::mpreal::set_default_prec
static void set_default_prec(mp_prec_t prec)
Definition: mpreal.h:2718
mpfr::mpreal::fabs
friend const mpreal fabs(const mpreal &v, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.h:2187
mpfr::mpreal::to_string
std::string to_string(size_t n=0, int b=default_base, mp_rnd_t mode=default_rnd) const
Definition: mpreal.cc:292
mpfr::atan
const mpreal atan(const mpreal &v, mp_rnd_t rnd_mode)
Definition: mpreal.h:2316
mpfr::mpreal::operator=
mpreal & operator=(const mpreal &v)
Definition: mpreal.h:671
mpfr::mpreal::_isinf
friend bool _isinf(const mpreal &v)
Definition: mpreal.h:1940
mpfr::mpreal::operator<<=
mpreal & operator<<=(const unsigned long int u)
Definition: mpreal.h:1425
mpfr::mpreal::cosh
friend const mpreal cosh(const mpreal &v, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.h:2338
mpfr::mpreal::lngamma
friend const mpreal lngamma(const mpreal &v, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.h:2436
mpfr::nextbelow
const mpreal nextbelow(const mpreal &x)
Definition: mpreal.h:2695
mpfr::mpreal::const_log2
friend const mpreal const_log2(mp_prec_t prec=mpreal::default_prec, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.h:2555
mpfr::mpreal::operator<<
friend std::ostream & operator<<(std::ostream &os, const mpreal &v)
mpfr::frexp
const mpreal frexp(const mpreal &v, mp_exp_t *exp)
Definition: mpreal.h:2045
mpfr::mpreal::default_rnd
static mp_rnd_t default_rnd
Definition: mpreal.h:90
mpfr::operator-
const mpreal operator-(const mpreal &a, const mpreal &b)
Definition: mpreal.h:1007
mpfr::sech
const mpreal sech(const mpreal &v, mp_rnd_t rnd_mode)
Definition: mpreal.h:2359
mpfr::_iszero
bool _iszero(const mpreal &v)
Definition: mpreal.h:1950
mpfr::trunc
const mpreal trunc(const mpreal &v)
Definition: mpreal.h:2618
mpfr::mpreal::set_double_bits
static void set_double_bits(int dbits)
Definition: mpreal.h:2750
mpfr::mpreal::_isnum
friend bool _isnum(const mpreal &v)
Definition: mpreal.h:1945
mpfr::mpreal::dim
friend const mpreal dim(const mpreal &a, const mpreal &b, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.h:2201
mpfr::mpreal::set_inf
void set_inf(int sign=+1)
Definition: mpreal.h:2025
mpfr::_y0
const mpreal _y0(const mpreal &v, mp_rnd_t rnd_mode)
Definition: mpreal.h:2492
mpfr::const_log2
const mpreal const_log2(mp_prec_t prec, mp_rnd_t rnd_mode)
Definition: mpreal.h:2555
mpfr::mpreal::pow
friend const mpreal pow(const mpreal &a, const mpreal &b, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.h:2767
mpfr::gamma
const mpreal gamma(const mpreal &v, mp_rnd_t rnd_mode)
Definition: mpreal.h:2429
mpfr::atanh
const mpreal atanh(const mpreal &v, mp_rnd_t rnd_mode)
Definition: mpreal.h:2394
mpfr::round
const mpreal round(const mpreal &v)
Definition: mpreal.h:2611
mpfr::mpreal::operator++
mpreal & operator++()
Definition: mpreal.h:915
mpfr::mpreal::trunc
friend const mpreal trunc(const mpreal &v)
Definition: mpreal.h:2618
mpfr::mpreal::~mpreal
~mpreal()
Definition: mpreal.cc:160
mpfr::mpreal::fits_in_bits
bool fits_in_bits(double x, int n)
Definition: mpreal.h:2760
mpfr::mpreal::const_euler
friend const mpreal const_euler(mp_prec_t prec=mpreal::default_prec, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.h:2571
mpfr::mpreal::log1p
friend const mpreal log1p(const mpreal &v, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.h:2408
mpfr::mpreal::set_exp
int set_exp(mp_exp_t e)
Definition: mpreal.h:2040
mpfr::sqrt
const mpreal sqrt(const unsigned int v, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.h:2146
mpfr::mul_2ui
const mpreal mul_2ui(const mpreal &v, unsigned long int k, mp_rnd_t rnd_mode)
Definition: mpreal.h:1514
mpfr::sin
const mpreal sin(const mpreal &v, mp_rnd_t rnd_mode)
Definition: mpreal.h:2262
mpfr::mpreal::erf
friend const mpreal erf(const mpreal &v, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.h:2457
mpfr::mpreal::operator+
const mpreal operator+() const
Definition: mpreal.h:802
mpfr::mpreal::round
friend const mpreal round(const mpreal &v)
Definition: mpreal.h:2611
mpfr::mpreal::const_catalan
friend const mpreal const_catalan(mp_prec_t prec=mpreal::default_prec, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.h:2579
mpfr::const_pi
const mpreal const_pi(mp_prec_t prec, mp_rnd_t rnd_mode)
Definition: mpreal.h:2563
mpfr::mpreal::rint_ceil
friend const mpreal rint_ceil(const mpreal &v, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.h:2625
mpfr::mpreal::set_emin
static int set_emin(mp_exp_t exp)
Definition: mpreal.h:2087
mpfr::expm1
const mpreal expm1(const mpreal &v, mp_rnd_t rnd_mode)
Definition: mpreal.h:2415
mpfr::mpreal::erfc
friend const mpreal erfc(const mpreal &v, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.h:2464
mpfr::_isinf
bool _isinf(const mpreal &v)
Definition: mpreal.h:1940
mpfr::mpreal::_jn
friend const mpreal _jn(long n, const mpreal &v, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.h:2485
mpfr::mpreal::rint_round
friend const mpreal rint_round(const mpreal &v, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.h:2639
mpfr::csch
const mpreal csch(const mpreal &v, mp_rnd_t rnd_mode)
Definition: mpreal.h:2366
mpfr::mpreal::get_emax_min
static mp_exp_t get_emax_min(void)
Definition: mpreal.h:2112
mpfr::mpreal::sech
friend const mpreal sech(const mpreal &v, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.h:2359
mpfr::tan
const mpreal tan(const mpreal &v, mp_rnd_t rnd_mode)
Definition: mpreal.h:2269
mpfr::mpreal::check_range
int check_range(int t, mp_rnd_t rnd_mode=default_rnd)
Definition: mpreal.h:2072
mpfr::div_2si
const mpreal div_2si(const mpreal &v, long int k, mp_rnd_t rnd_mode)
Definition: mpreal.h:1536
mpfr::mpreal::atan
friend const mpreal atan(const mpreal &v, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.h:2316
mpfr::mpreal::operator+=
mpreal & operator+=(const mpreal &v)
Definition: mpreal.h:739
mpfr::mpreal::exp2
friend const mpreal exp2(const mpreal &v, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.h:2241
mpfr::log1p
const mpreal log1p(const mpreal &v, mp_rnd_t rnd_mode)
Definition: mpreal.h:2408
mpfr::mpreal::rec_sqrt
friend const mpreal rec_sqrt(const mpreal &v, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.h:2544
mpfr::mpreal::remquo
friend const mpreal remquo(long *q, const mpreal &x, const mpreal &y, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.cc:269
mpfr::operator+
const mpreal operator+(const mpreal &a, const mpreal &b)
Definition: mpreal.h:807
mpfr::mpreal::min
friend const mpreal min(const mpreal &x, const mpreal &y)
Definition: mpreal.h:2675
mpfr::mpreal::sqr
friend const mpreal sqr(const mpreal &v, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.h:2125
mpfr::sin_cos
int sin_cos(mpreal &s, mpreal &c, const mpreal &v, mp_rnd_t rnd_mode)
Definition: mpreal.h:2297
mpfr::div_2ui
const mpreal div_2ui(const mpreal &v, unsigned long int k, mp_rnd_t rnd_mode)
Definition: mpreal.h:1529
mpfr::mpreal::eint
friend const mpreal eint(const mpreal &v, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.h:2422
mpfr::csc
const mpreal csc(const mpreal &v, mp_rnd_t rnd_mode)
Definition: mpreal.h:2283
mpfr::mpreal::_y0
friend const mpreal _y0(const mpreal &v, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.h:2492
mpfr::lgamma
const mpreal lgamma(const mpreal &v, int *signp, mp_rnd_t rnd_mode)
Definition: mpreal.h:2443
mpfr::mpreal::sec
friend const mpreal sec(const mpreal &v, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.h:2276
mpfr::urandomb
const mpreal urandomb(gmp_randstate_t &state)
Definition: mpreal.h:2702
mpfr::tanh
const mpreal tanh(const mpreal &v, mp_rnd_t rnd_mode)
Definition: mpreal.h:2352
mpfr::mpreal::tan
friend const mpreal tan(const mpreal &v, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.h:2269
mpfr::mpreal::exp10
friend const mpreal exp10(const mpreal &v, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.h:2248
mpfr::const_catalan
const mpreal const_catalan(mp_prec_t prec, mp_rnd_t rnd_mode)
Definition: mpreal.h:2579
mpfr::asin
const mpreal asin(const mpreal &v, mp_rnd_t rnd_mode)
Definition: mpreal.h:2309
mpfr::mpreal::operator>=
friend bool operator>=(const mpreal &a, const mpreal &b)
Definition: mpreal.h:1610
mpfr::coth
const mpreal coth(const mpreal &v, mp_rnd_t rnd_mode)
Definition: mpreal.h:2373
mpfr::mpreal::_yn
friend const mpreal _yn(long n, const mpreal &v, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.h:2506
mpfr::mpreal::nextbelow
friend const mpreal nextbelow(const mpreal &x)
Definition: mpreal.h:2695
mpfr::operator>=
bool operator>=(const mpreal &a, const unsigned long int b)
Definition: mpreal.h:1615
mpfr::mpreal::ldexp
friend const mpreal ldexp(const mpreal &v, mp_exp_t exp)
Definition: mpreal.h:2053
mpfr::mpreal::atanh
friend const mpreal atanh(const mpreal &v, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.h:2394
mpfr::mpreal::sinh
friend const mpreal sinh(const mpreal &v, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.h:2345
mpfr::mpreal::frac
friend const mpreal frac(const mpreal &v, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.h:2653
mpfr::mpreal::csc
friend const mpreal csc(const mpreal &v, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.h:2283
mpfr::mpreal::log2
friend const mpreal log2(const mpreal &v, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.h:2220
mpfr::mpreal::rint
friend const mpreal rint(const mpreal &v, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.h:2589
mpfr::fabs
const mpreal fabs(const mpreal &v, mp_rnd_t rnd_mode)
Definition: mpreal.h:2187
mpfr::mpreal::div_2si
friend const mpreal div_2si(const mpreal &v, long int k, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.h:1536
c
const double c
Definition: gfit.cc:200
mpfr::mpreal::set_sign
void set_sign(int sign, mp_rnd_t rnd_mode=default_rnd)
Definition: mpreal.h:2010
b
FLOAT b(int j, FLOAT z)
Definition: y1.cc:79
mpfr::mpreal::ceil
friend const mpreal ceil(const mpreal &v)
Definition: mpreal.h:2596
mpfr::to_string
std::string to_string(T t, std::ios_base &(*f)(std::ios_base &))
Definition: mpreal.cc:285
mpfr::zeta
const mpreal zeta(const mpreal &v, mp_rnd_t rnd_mode)
Definition: mpreal.h:2450
mpfr::mpreal::get_default_prec
static mp_prec_t get_default_prec()
Definition: mpreal.h:2724
mpfr::mpreal::operator<
friend bool operator<(const mpreal &a, const mpreal &b)
Definition: mpreal.h:1675
std::swap
void swap(mpfr::mpreal &x, mpfr::mpreal &y)
Definition: mpreal.h:3069
mpfr::floor
const mpreal floor(const mpreal &v)
Definition: mpreal.h:2604
mpfr::mpreal::get_emin_max
static mp_exp_t get_emin_max(void)
Definition: mpreal.h:2107
mpfr::mpreal::log
friend const mpreal log(const mpreal &v, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.h:2213
mpfr::sinh
const mpreal sinh(const mpreal &v, mp_rnd_t rnd_mode)
Definition: mpreal.h:2345
mpfr::nextabove
const mpreal nextabove(const mpreal &x)
Definition: mpreal.h:2688
mpfr::mpreal::_j0
friend const mpreal _j0(const mpreal &v, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.h:2471
mpfr::mpreal::gamma
friend const mpreal gamma(const mpreal &v, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.h:2429
mpfr::mpreal::rint_floor
friend const mpreal rint_floor(const mpreal &v, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.h:2632
mpfr::root
const mpreal root(const mpreal &v, unsigned long int k, mp_rnd_t rnd_mode)
Definition: mpreal.h:2180
mpfr::mpreal::set_default_rnd
static void set_default_rnd(mp_rnd_t rnd_mode)
Definition: mpreal.h:2739
mpfr::operator/
const mpreal operator/(const mpreal &a, const mpreal &b)
Definition: mpreal.h:1323
mpfr::mpreal::csch
friend const mpreal csch(const mpreal &v, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.h:2366
mpfr::li2
const mpreal li2(const mpreal &v, mp_rnd_t rnd_mode)
Definition: mpreal.h:2522
mpfr::mpreal::log10
friend const mpreal log10(const mpreal &v, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.h:2227
mpfr::mpreal::sinh_cosh
friend int sinh_cosh(mpreal &s, mpreal &c, const mpreal &v, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.h:2517
mpfr::mpreal::asin
friend const mpreal asin(const mpreal &v, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.h:2309
mpfr::mpreal::operator-=
mpreal & operator-=(const mpreal &v)
Definition: mpreal.h:943
mpfr::_isnum
bool _isnum(const mpreal &v)
Definition: mpreal.h:1945
mpfr::mpreal::fmod
friend const mpreal fmod(const mpreal &x, const mpreal &y, mp_rnd_t rnd_mode=mpreal::default_rnd)
Definition: mpreal.h:2529
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