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222 	friend const mpreal operator-(const unsigned long int b, const mpreal& a);

223 friend const mpreal operator-(const unsigned int b, const mpreal& a);
224 friend const mpreal operator-(const long int b, const mpreal& a);
225 friend const mpreal operator-(const int b, const mpreal& a);
226 friend const mpreal operator-(const double b, const mpreal& a);
251 friend const mpreal operator/(const unsigned long int b, const mpreal& a);
252 friend const mpreal operator/(const unsigned int b, const mpreal& a);
253 friend const mpreal operator/(const long int b, const mpreal& a);
254 friend const mpreal operator/(const int b, const mpreal& a);
255 friend const mpreal operator/(const double b, const mpreal& a);
270 friend bool operator > (const mpreal& a, const mpreal& b);
271 friend bool operator >= (const mpreal& a, const mpreal& b);
272 friend bool operator < (const mpreal& a, const mpreal& b);
273 friend bool operator <= (const mpreal& a, const mpreal& b);
274 friend bool operator == (const mpreal& a, const mpreal& b);
275 friend bool operator != (const mpreal& a, const mpreal& b);
278 friend bool operator == (const mpreal& a, const unsigned long int b);
279 friend bool operator == (const mpreal& a, const unsigned int b);
280 friend bool operator == (const mpreal& a, const long int b);
281 friend bool operator == (const mpreal& a, const int b);
282 friend bool operator == (const mpreal& a, const long double b);
283 friend bool operator == (const mpreal& a, const double b);
309 friend const mpreal sqr (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
310 friend const mpreal sqrt(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
311 friend const mpreal sqrt(const unsigned long int v, mp_rnd_t rnd_mode = mpreal::default_rnd);
312 friend const mpreal cbrt(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
313 friend const mpreal root(const mpreal& v, unsigned long int k, mp_rnd_t rnd_mode = mpreal::default_rnd);
314 friend const mpreal pow (const mpreal& a, const mpreal& b, mp_rnd_t rnd_mode = mpreal::default_rnd);
315 friend const mpreal pow (const mpreal& a, const mpz_t b, mp_rnd_t rnd_mode = mpreal::default_rnd);
316 friend const mpreal pow (const mpreal& a, const unsigned long int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
317 friend const mpreal pow (const mpreal& a, const long int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
318 friend const mpreal pow (const unsigned long int a, const mpreal& b, mp_rnd_t rnd_mode = mpreal::default_rnd);
319 friend const mpreal pow (const unsigned long int a, const unsigned long int b, mp_rnd_t rnd_mode = mpreal::default_rnd);
320 friend const mpreal fabs(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
322 friend const mpreal abs(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
323 friend const mpreal dim(const mpreal& a, const mpreal& b, mp_rnd_t rnd_mode = mpreal::default_rnd);
324 friend inline const mpreal mul_2ui(const mpreal& v, unsigned long int k, mp_rnd_t rnd_mode = mpreal::default_rnd);
325 friend inline const mpreal mul_2si(const mpreal& v, long int k, mp_rnd_t rnd_mode = mpreal::default_rnd);
326 friend inline const mpreal div_2ui(const mpreal& v, unsigned long int k, mp_rnd_t rnd_mode = mpreal::default_rnd);
327 friend inline const mpreal div_2si(const mpreal& v, long int k, mp_rnd_t rnd_mode = mpreal::default_rnd);
328 friend int cmpabs(const mpreal& a,const mpreal& b);
330 friend const mpreal log (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
331 friend const mpreal log2 (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
332 friend const mpreal log10(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
333 friend const mpreal exp (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
334 friend const mpreal exp2 (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
335 friend const mpreal exp10(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
336 friend const mpreal log1p(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
337 friend const mpreal expm1(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
339 friend const mpreal cos(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
340 friend const mpreal sin(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
341 friend const mpreal tan(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
342 friend const mpreal sec(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
343 friend const mpreal csc(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
344 friend const mpreal cot(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
345 friend int sin_cos(mpreal& s, mpreal& c, const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
347 friend const mpreal acos (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
348 friend const mpreal asin (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
349 friend const mpreal atan (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
350 friend const mpreal atan2 (const mpreal& y, const mpreal& x, mp_rnd_t rnd_mode = mpreal::default_rnd);
351 friend const mpreal acot (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
352 friend const mpreal asec (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
353 friend const mpreal acsc (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
355 friend const mpreal cosh (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
356 friend const mpreal sinh (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
357 friend const mpreal tanh (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
358 friend const mpreal sech (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
359 friend const mpreal csch (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
360 friend
361 friend const mpreal acosh (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
362 friend const mpreal asinh (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
363 friend const mpreal atanh (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
364 friend const mpreal acoth (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
365 friend const mpreal asech (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
366 friend const mpreal acsch (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
368 friend const mpreal hypot (const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode = mpreal::default_rnd);
370 friend const mpreal fac_ui (unsigned long int v, mp_prec_t prec = mpreal::default_prec, mp_rnd_t rnd_mode = mpreal::default_rnd);
371 friend const mpreal eint (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
373 friend const mpreal gamma (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
374 friend const mpreal lngamma (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
375 friend const mpreal lgamma (const mpreal& v, int *signp = 0, mp_rnd_t rnd_mode = mpreal::default_rnd);
376 friend const mpreal zeta (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
377 friend const mpreal erf (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
378 friend const mpreal erfc (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
379 friend const mpreal besselj0 (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
380 friend const mpreal besselj1 (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
381 friend const mpreal besseljn (long n, const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
382 friend const mpreal bessely0 (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
383 friend const mpreal bessely1 (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
384 friend const mpreal besselyn (long n, const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
385 friend const mpreal fma (const mpreal& v1, const mpreal& v2, const mpreal& v3, mp_rnd_t rnd_mode = mpreal::default_rnd);
386 friend const mpreal fms (const mpreal& v1, const mpreal& v2, const mpreal& v3, mp_rnd_t rnd_mode = mpreal::default_rnd);
387 friend const mpreal agm (const mpreal& v1, const mpreal& v2, mp_rnd_t rnd_mode = mpreal::default_rnd);
388 friend const mpreal sum (const mpreal tab[], unsigned long int n, mp_rnd_t rnd_mode = mpreal::default_rnd);
389 friend int sgn(const mpreal& v); // -1 or +1
393 friend int sinh_cosh(mpreal& s, mpreal& c, const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
394 friend const mpreal li2(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
395 friend const mpreal fmod (const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode = mpreal::default_rnd);
396 friend const mpreal rec_sqrt(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
401 friend const mpreal digamma(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
402 friend const mpreal ai(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
403 friend const mpreal urandom (gmp_randstate_t& state,mp_rnd_t rnd_mode = mpreal::default_rnd); // use gmp_randinit_default() to init state, gmp_randclear() to clear
404 friend bool isregular(const mpreal& v);
411 friend const mpreal random(unsigned int seed = 0);
414 friend const mpreal frexp(const mpreal& v, mp_exp_t* exp);
415 friend const mpreal ldexp(const mpreal& v, mp_exp_t exp);
419 friend const mpreal modf(const mpreal& v, mpreal& n);
423 friend const mpreal const_log2 (mp_prec_t prec = mpreal::default_prec, mp_rnd_t rnd_mode = mpreal::default_rnd);
424 friend const mpreal const_pi (mp_prec_t prec = mpreal::default_prec, mp_rnd_t rnd_mode = mpreal::default_rnd);
425 friend const mpreal const_euler (mp_prec_t prec = mpreal::default_prec, mp_rnd_t rnd_mode = mpreal::default_rnd);
426 friend const mpreal const_catalan (mp_prec_t prec = mpreal::default_prec, mp_rnd_t rnd_mode = mpreal::default_rnd);
428 friend const mpreal const_infinity(int sign = 1, mp_prec_t prec = mpreal::default_prec, mp_rnd_t rnd_mode = mpreal::default_rnd);
431 friend std::ostream& operator<<(std::ostream& os, const mpreal& v);
432 friend std::istream& operator>>(std::istream& is, mpreal& v);
435 friend const mpreal rint (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
436 friend const mpreal ceil (const mpreal& v);
437 friend const mpreal floor(const mpreal& v);
438 friend const mpreal round(const mpreal& v);
439 friend const mpreal trunc(const mpreal& v);
440 friend const mpreal rint_ceil (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
441 friend const mpreal rint_floor(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
442 friend const mpreal rint_round(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
443 friend const mpreal rint_trunc(const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
444 friend const mpreal frac (const mpreal& v, mp_rnd_t rnd_mode = mpreal::default_rnd);
445 friend const mpreal remainder (const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode = mpreal::default_rnd);
446 friend const mpreal remquo (long* q, const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode = mpreal::default_rnd);
449 friend const mpreal nexttoward (const mpreal& x, const mpreal& y);
450 friend const mpreal nextabove (const mpreal& x);
451 friend const mpreal nextbelow (const mpreal& x);
454 friend const mpreal urandomb (gmp_randstate_t& state);
458 friend const mpreal random2 (mp_size_t size, mp_exp_t exp);
462 friend bool isnan (const mpreal& v);
463 friend bool isinf (const mpreal& v);
464 friend bool isfinite(const mpreal& v);
466 friend bool isnum(const mpreal& v);
467 friend bool iszero(const mpreal& v);
468 friend bool isint(const mpreal& v);
512 friend void swap(mpreal& x, mpreal& y);
516 friend const mpreal fmax(const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode = default_rnd);
517 friend const mpreal fmin(const mpreal& x, const mpreal& y, mp_rnd_t rnd_mode = default_rnd);