1/* Implementations of operations between mpfr and mpz/mpq data 2 3Copyright 2001, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013 Free Software Foundation, Inc. 4Contributed by the AriC and Caramel projects, INRIA. 5 6This file is part of the GNU MPFR Library. 7 8The GNU MPFR Library is free software; you can redistribute it and/or modify 9it under the terms of the GNU Lesser General Public License as published by 10the Free Software Foundation; either version 3 of the License, or (at your 11option) any later version. 12 13The GNU MPFR Library is distributed in the hope that it will be useful, but 14WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY 15or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public 16License for more details. 17 18You should have received a copy of the GNU Lesser General Public License 19along with the GNU MPFR Library; see the file COPYING.LESSER. If not, see 20http://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc., 2151 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */ 22 23#define MPFR_NEED_LONGLONG_H 24#include "mpfr-impl.h" 25 26/* Init and set a mpfr_t with enough precision to store a mpz. 27 This function should be called in the extended exponent range. */ 28static void 29init_set_z (mpfr_ptr t, mpz_srcptr z) 30{ 31 mpfr_prec_t p; 32 int i; 33 34 if (mpz_size (z) <= 1) 35 p = GMP_NUMB_BITS; 36 else 37 MPFR_MPZ_SIZEINBASE2 (p, z); 38 mpfr_init2 (t, p); 39 i = mpfr_set_z (t, z, MPFR_RNDN); 40 /* Possible assertion failure in case of overflow. Such cases, 41 which imply that z is huge (if the function is called in 42 the extended exponent range), are currently not supported, 43 just like precisions around MPFR_PREC_MAX. */ 44 MPFR_ASSERTN (i == 0); (void) i; /* use i to avoid a warning */ 45} 46 47/* Init, set a mpfr_t with enough precision to store a mpz_t without round, 48 call the function, and clear the allocated mpfr_t */ 49static int 50foo (mpfr_ptr x, mpfr_srcptr y, mpz_srcptr z, mpfr_rnd_t r, 51 int (*f)(mpfr_ptr, mpfr_srcptr, mpfr_srcptr, mpfr_rnd_t)) 52{ 53 mpfr_t t; 54 int i; 55 MPFR_SAVE_EXPO_DECL (expo); 56 57 MPFR_SAVE_EXPO_MARK (expo); 58 init_set_z (t, z); /* There should be no exceptions. */ 59 i = (*f) (x, y, t, r); 60 MPFR_SAVE_EXPO_UPDATE_FLAGS (expo, __gmpfr_flags); 61 mpfr_clear (t); 62 MPFR_SAVE_EXPO_FREE (expo); 63 return mpfr_check_range (x, i, r); 64} 65 66static int 67foo2 (mpfr_ptr x, mpz_srcptr y, mpfr_srcptr z, mpfr_rnd_t r, 68 int (*f)(mpfr_ptr, mpfr_srcptr, mpfr_srcptr, mpfr_rnd_t)) 69{ 70 mpfr_t t; 71 int i; 72 MPFR_SAVE_EXPO_DECL (expo); 73 74 MPFR_SAVE_EXPO_MARK (expo); 75 init_set_z (t, y); /* There should be no exceptions. */ 76 i = (*f) (x, t, z, r); 77 MPFR_SAVE_EXPO_UPDATE_FLAGS (expo, __gmpfr_flags); 78 mpfr_clear (t); 79 MPFR_SAVE_EXPO_FREE (expo); 80 return mpfr_check_range (x, i, r); 81} 82 83int 84mpfr_mul_z (mpfr_ptr y, mpfr_srcptr x, mpz_srcptr z, mpfr_rnd_t r) 85{ 86 return foo (y, x, z, r, mpfr_mul); 87} 88 89int 90mpfr_div_z (mpfr_ptr y, mpfr_srcptr x, mpz_srcptr z, mpfr_rnd_t r) 91{ 92 return foo (y, x, z, r, mpfr_div); 93} 94 95int 96mpfr_add_z (mpfr_ptr y, mpfr_srcptr x, mpz_srcptr z, mpfr_rnd_t r) 97{ 98 /* Mpz 0 is unsigned */ 99 if (MPFR_UNLIKELY (mpz_sgn (z) == 0)) 100 return mpfr_set (y, x, r); 101 else 102 return foo (y, x, z, r, mpfr_add); 103} 104 105int 106mpfr_sub_z (mpfr_ptr y, mpfr_srcptr x, mpz_srcptr z, mpfr_rnd_t r) 107{ 108 /* Mpz 0 is unsigned */ 109 if (MPFR_UNLIKELY (mpz_sgn (z) == 0)) 110 return mpfr_set (y, x, r); 111 else 112 return foo (y, x, z, r, mpfr_sub); 113} 114 115int 116mpfr_z_sub (mpfr_ptr y, mpz_srcptr x, mpfr_srcptr z, mpfr_rnd_t r) 117{ 118 /* Mpz 0 is unsigned */ 119 if (MPFR_UNLIKELY (mpz_sgn (x) == 0)) 120 return mpfr_neg (y, z, r); 121 else 122 return foo2 (y, x, z, r, mpfr_sub); 123} 124 125int 126mpfr_cmp_z (mpfr_srcptr x, mpz_srcptr z) 127{ 128 mpfr_t t; 129 int res; 130 mpfr_prec_t p; 131 unsigned int flags; 132 133 if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x))) 134 return mpfr_cmp_si (x, mpz_sgn (z)); 135 136 if (mpz_size (z) <= 1) 137 p = GMP_NUMB_BITS; 138 else 139 MPFR_MPZ_SIZEINBASE2 (p, z); 140 mpfr_init2 (t, p); 141 flags = __gmpfr_flags; 142 if (mpfr_set_z (t, z, MPFR_RNDN)) 143 { 144 /* overflow (t is an infinity) or underflow */ 145 mpfr_div_2ui (t, t, 2, MPFR_RNDZ); /* if underflow, set t to zero */ 146 __gmpfr_flags = flags; /* restore the flags */ 147 /* The real value of t (= z), which falls outside the exponent range, 148 has been replaced by an equivalent value for the comparison: zero 149 or an infinity. */ 150 } 151 res = mpfr_cmp (x, t); 152 mpfr_clear (t); 153 return res; 154} 155 156/* Compute y = RND(x*n/d), where n and d are mpz integers. 157 An integer 0 is assumed to have a positive sign. 158 This function is used by mpfr_mul_q and mpfr_div_q. 159 Note: the status of the rational 0/(-1) is not clear (if there is 160 a signed infinity, there should be a signed zero). But infinities 161 are not currently supported/documented in GMP, and if the rational 162 is canonicalized as it should be, the case 0/(-1) cannot occur. */ 163static int 164mpfr_muldiv_z (mpfr_ptr y, mpfr_srcptr x, mpz_srcptr n, mpz_srcptr d, 165 mpfr_rnd_t rnd_mode) 166{ 167 if (MPFR_UNLIKELY (mpz_sgn (n) == 0)) 168 { 169 if (MPFR_UNLIKELY (mpz_sgn (d) == 0)) 170 MPFR_SET_NAN (y); 171 else 172 { 173 mpfr_mul_ui (y, x, 0, MPFR_RNDN); /* exact: +0, -0 or NaN */ 174 if (MPFR_UNLIKELY (mpz_sgn (d) < 0)) 175 MPFR_CHANGE_SIGN (y); 176 } 177 return 0; 178 } 179 else if (MPFR_UNLIKELY (mpz_sgn (d) == 0)) 180 { 181 mpfr_div_ui (y, x, 0, MPFR_RNDN); /* exact: +Inf, -Inf or NaN */ 182 if (MPFR_UNLIKELY (mpz_sgn (n) < 0)) 183 MPFR_CHANGE_SIGN (y); 184 return 0; 185 } 186 else 187 { 188 mpfr_prec_t p; 189 mpfr_t tmp; 190 int inexact; 191 MPFR_SAVE_EXPO_DECL (expo); 192 193 MPFR_SAVE_EXPO_MARK (expo); 194 195 /* With the current MPFR code, using mpfr_mul_z and mpfr_div_z 196 for the general case should be faster than doing everything 197 in mpn, mpz and/or mpq. MPFR_SAVE_EXPO_MARK could be avoided 198 here, but it would be more difficult to handle corner cases. */ 199 MPFR_MPZ_SIZEINBASE2 (p, n); 200 mpfr_init2 (tmp, MPFR_PREC (x) + p); 201 inexact = mpfr_mul_z (tmp, x, n, MPFR_RNDN); 202 /* Since |n| >= 1, an underflow is not possible. And the precision of 203 tmp has been chosen so that inexact != 0 iff there's an overflow. */ 204 if (MPFR_UNLIKELY (inexact != 0)) 205 { 206 mpfr_t x0; 207 mpfr_exp_t ex; 208 MPFR_BLOCK_DECL (flags); 209 210 /* intermediate overflow case */ 211 MPFR_ASSERTD (mpfr_inf_p (tmp)); 212 ex = MPFR_GET_EXP (x); /* x is a pure FP number */ 213 MPFR_ALIAS (x0, x, MPFR_SIGN(x), 0); /* x0 = x / 2^ex */ 214 MPFR_BLOCK (flags, 215 inexact = mpfr_mul_z (tmp, x0, n, MPFR_RNDN); 216 MPFR_ASSERTD (inexact == 0); 217 inexact = mpfr_div_z (y, tmp, d, rnd_mode); 218 /* Just in case the division underflows 219 (highly unlikely, not supported)... */ 220 MPFR_ASSERTN (!MPFR_BLOCK_EXCEP)); 221 MPFR_EXP (y) += ex; 222 /* Detect highly unlikely, not supported corner cases... */ 223 MPFR_ASSERTN (MPFR_EXP (y) >= __gmpfr_emin && MPFR_IS_PURE_FP (y)); 224 /* The potential overflow will be detected by mpfr_check_range. */ 225 } 226 else 227 inexact = mpfr_div_z (y, tmp, d, rnd_mode); 228 229 mpfr_clear (tmp); 230 231 MPFR_SAVE_EXPO_FREE (expo); 232 return mpfr_check_range (y, inexact, rnd_mode); 233 } 234} 235 236int 237mpfr_mul_q (mpfr_ptr y, mpfr_srcptr x, mpq_srcptr z, mpfr_rnd_t rnd_mode) 238{ 239 return mpfr_muldiv_z (y, x, mpq_numref (z), mpq_denref (z), rnd_mode); 240} 241 242int 243mpfr_div_q (mpfr_ptr y, mpfr_srcptr x, mpq_srcptr z, mpfr_rnd_t rnd_mode) 244{ 245 return mpfr_muldiv_z (y, x, mpq_denref (z), mpq_numref (z), rnd_mode); 246} 247 248int 249mpfr_add_q (mpfr_ptr y, mpfr_srcptr x, mpq_srcptr z, mpfr_rnd_t rnd_mode) 250{ 251 mpfr_t t,q; 252 mpfr_prec_t p; 253 mpfr_exp_t err; 254 int res; 255 MPFR_SAVE_EXPO_DECL (expo); 256 MPFR_ZIV_DECL (loop); 257 258 if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x))) 259 { 260 if (MPFR_IS_NAN (x)) 261 { 262 MPFR_SET_NAN (y); 263 MPFR_RET_NAN; 264 } 265 else if (MPFR_IS_INF (x)) 266 { 267 if (MPFR_UNLIKELY (mpz_sgn (mpq_denref (z)) == 0 && 268 MPFR_MULT_SIGN (mpz_sgn (mpq_numref (z)), 269 MPFR_SIGN (x)) <= 0)) 270 { 271 MPFR_SET_NAN (y); 272 MPFR_RET_NAN; 273 } 274 MPFR_SET_INF (y); 275 MPFR_SET_SAME_SIGN (y, x); 276 MPFR_RET (0); 277 } 278 else 279 { 280 MPFR_ASSERTD (MPFR_IS_ZERO (x)); 281 if (MPFR_UNLIKELY (mpq_sgn (z) == 0)) 282 return mpfr_set (y, x, rnd_mode); /* signed 0 - Unsigned 0 */ 283 else 284 return mpfr_set_q (y, z, rnd_mode); 285 } 286 } 287 288 MPFR_SAVE_EXPO_MARK (expo); 289 290 p = MPFR_PREC (y) + 10; 291 mpfr_init2 (t, p); 292 mpfr_init2 (q, p); 293 294 MPFR_ZIV_INIT (loop, p); 295 for (;;) 296 { 297 MPFR_BLOCK_DECL (flags); 298 299 res = mpfr_set_q (q, z, MPFR_RNDN); /* Error <= 1/2 ulp(q) */ 300 /* If z if @INF@ (1/0), res = 0, so it quits immediately */ 301 if (MPFR_UNLIKELY (res == 0)) 302 /* Result is exact so we can add it directly! */ 303 { 304 res = mpfr_add (y, x, q, rnd_mode); 305 break; 306 } 307 MPFR_BLOCK (flags, mpfr_add (t, x, q, MPFR_RNDN)); 308 /* Error on t is <= 1/2 ulp(t), except in case of overflow/underflow, 309 but such an exception is very unlikely as it would be possible 310 only if q has a huge numerator or denominator. Not supported! */ 311 MPFR_ASSERTN (! (MPFR_OVERFLOW (flags) || MPFR_UNDERFLOW (flags))); 312 /* Error / ulp(t) <= 1/2 + 1/2 * 2^(EXP(q)-EXP(t)) 313 If EXP(q)-EXP(t)>0, <= 2^(EXP(q)-EXP(t)-1)*(1+2^-(EXP(q)-EXP(t))) 314 <= 2^(EXP(q)-EXP(t)) 315 If EXP(q)-EXP(t)<0, <= 2^0 */ 316 /* We can get 0, but we can't round since q is inexact */ 317 if (MPFR_LIKELY (!MPFR_IS_ZERO (t))) 318 { 319 err = (mpfr_exp_t) p - 1 - MAX (MPFR_GET_EXP(q)-MPFR_GET_EXP(t), 0); 320 if (MPFR_LIKELY (MPFR_CAN_ROUND (t, err, MPFR_PREC (y), rnd_mode))) 321 { 322 res = mpfr_set (y, t, rnd_mode); 323 break; 324 } 325 } 326 MPFR_ZIV_NEXT (loop, p); 327 mpfr_set_prec (t, p); 328 mpfr_set_prec (q, p); 329 } 330 MPFR_ZIV_FREE (loop); 331 mpfr_clear (t); 332 mpfr_clear (q); 333 334 MPFR_SAVE_EXPO_FREE (expo); 335 return mpfr_check_range (y, res, rnd_mode); 336} 337 338int 339mpfr_sub_q (mpfr_ptr y, mpfr_srcptr x, mpq_srcptr z,mpfr_rnd_t rnd_mode) 340{ 341 mpfr_t t,q; 342 mpfr_prec_t p; 343 int res; 344 mpfr_exp_t err; 345 MPFR_SAVE_EXPO_DECL (expo); 346 MPFR_ZIV_DECL (loop); 347 348 if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x))) 349 { 350 if (MPFR_IS_NAN (x)) 351 { 352 MPFR_SET_NAN (y); 353 MPFR_RET_NAN; 354 } 355 else if (MPFR_IS_INF (x)) 356 { 357 if (MPFR_UNLIKELY (mpz_sgn (mpq_denref (z)) == 0 && 358 MPFR_MULT_SIGN (mpz_sgn (mpq_numref (z)), 359 MPFR_SIGN (x)) >= 0)) 360 { 361 MPFR_SET_NAN (y); 362 MPFR_RET_NAN; 363 } 364 MPFR_SET_INF (y); 365 MPFR_SET_SAME_SIGN (y, x); 366 MPFR_RET (0); 367 } 368 else 369 { 370 MPFR_ASSERTD (MPFR_IS_ZERO (x)); 371 372 if (MPFR_UNLIKELY (mpq_sgn (z) == 0)) 373 return mpfr_set (y, x, rnd_mode); /* signed 0 - Unsigned 0 */ 374 else 375 { 376 res = mpfr_set_q (y, z, MPFR_INVERT_RND (rnd_mode)); 377 MPFR_CHANGE_SIGN (y); 378 return -res; 379 } 380 } 381 } 382 383 MPFR_SAVE_EXPO_MARK (expo); 384 385 p = MPFR_PREC (y) + 10; 386 mpfr_init2 (t, p); 387 mpfr_init2 (q, p); 388 389 MPFR_ZIV_INIT (loop, p); 390 for(;;) 391 { 392 MPFR_BLOCK_DECL (flags); 393 394 res = mpfr_set_q(q, z, MPFR_RNDN); /* Error <= 1/2 ulp(q) */ 395 /* If z if @INF@ (1/0), res = 0, so it quits immediately */ 396 if (MPFR_UNLIKELY (res == 0)) 397 /* Result is exact so we can add it directly!*/ 398 { 399 res = mpfr_sub (y, x, q, rnd_mode); 400 break; 401 } 402 MPFR_BLOCK (flags, mpfr_sub (t, x, q, MPFR_RNDN)); 403 /* Error on t is <= 1/2 ulp(t), except in case of overflow/underflow, 404 but such an exception is very unlikely as it would be possible 405 only if q has a huge numerator or denominator. Not supported! */ 406 MPFR_ASSERTN (! (MPFR_OVERFLOW (flags) || MPFR_UNDERFLOW (flags))); 407 /* Error / ulp(t) <= 1/2 + 1/2 * 2^(EXP(q)-EXP(t)) 408 If EXP(q)-EXP(t)>0, <= 2^(EXP(q)-EXP(t)-1)*(1+2^-(EXP(q)-EXP(t))) 409 <= 2^(EXP(q)-EXP(t)) 410 If EXP(q)-EXP(t)<0, <= 2^0 */ 411 /* We can get 0, but we can't round since q is inexact */ 412 if (MPFR_LIKELY (!MPFR_IS_ZERO (t))) 413 { 414 err = (mpfr_exp_t) p - 1 - MAX (MPFR_GET_EXP(q)-MPFR_GET_EXP(t), 0); 415 res = MPFR_CAN_ROUND (t, err, MPFR_PREC (y), rnd_mode); 416 if (MPFR_LIKELY (res != 0)) /* We can round! */ 417 { 418 res = mpfr_set (y, t, rnd_mode); 419 break; 420 } 421 } 422 MPFR_ZIV_NEXT (loop, p); 423 mpfr_set_prec (t, p); 424 mpfr_set_prec (q, p); 425 } 426 MPFR_ZIV_FREE (loop); 427 mpfr_clear (t); 428 mpfr_clear (q); 429 430 MPFR_SAVE_EXPO_FREE (expo); 431 return mpfr_check_range (y, res, rnd_mode); 432} 433 434int 435mpfr_cmp_q (mpfr_srcptr x, mpq_srcptr q) 436{ 437 mpfr_t t; 438 int res; 439 mpfr_prec_t p; 440 MPFR_SAVE_EXPO_DECL (expo); 441 442 if (MPFR_UNLIKELY (mpq_denref (q) == 0)) 443 { 444 /* q is an infinity or NaN */ 445 mpfr_init2 (t, 2); 446 mpfr_set_q (t, q, MPFR_RNDN); 447 res = mpfr_cmp (x, t); 448 mpfr_clear (t); 449 return res; 450 } 451 452 if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x))) 453 return mpfr_cmp_si (x, mpq_sgn (q)); 454 455 MPFR_SAVE_EXPO_MARK (expo); 456 457 /* x < a/b ? <=> x*b < a */ 458 MPFR_MPZ_SIZEINBASE2 (p, mpq_denref (q)); 459 mpfr_init2 (t, MPFR_PREC(x) + p); 460 res = mpfr_mul_z (t, x, mpq_denref (q), MPFR_RNDN); 461 MPFR_ASSERTD (res == 0); 462 res = mpfr_cmp_z (t, mpq_numref (q)); 463 mpfr_clear (t); 464 465 MPFR_SAVE_EXPO_FREE (expo); 466 return res; 467} 468 469int 470mpfr_cmp_f (mpfr_srcptr x, mpf_srcptr z) 471{ 472 mpfr_t t; 473 int res; 474 MPFR_SAVE_EXPO_DECL (expo); 475 476 if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x))) 477 return mpfr_cmp_si (x, mpf_sgn (z)); 478 479 MPFR_SAVE_EXPO_MARK (expo); 480 481 mpfr_init2 (t, MPFR_PREC_MIN + ABS(SIZ(z)) * GMP_NUMB_BITS ); 482 res = mpfr_set_f (t, z, MPFR_RNDN); 483 MPFR_ASSERTD (res == 0); 484 res = mpfr_cmp (x, t); 485 mpfr_clear (t); 486 487 MPFR_SAVE_EXPO_FREE (expo); 488 return res; 489} 490