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round_prec.c
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1 /* mpfr_round_raw_generic, mpfr_round_raw2, mpfr_round_raw, mpfr_prec_round,
2  mpfr_can_round, mpfr_can_round_raw -- various rounding functions
3 
4 Copyright 1999-2020 Free Software Foundation, Inc.
5 Contributed by the AriC and Caramba projects, INRIA.
6 
7 This file is part of the GNU MPFR Library.
8 
9 The GNU MPFR Library is free software; you can redistribute it and/or modify
10 it under the terms of the GNU Lesser General Public License as published by
11 the Free Software Foundation; either version 3 of the License, or (at your
12 option) any later version.
13 
14 The GNU MPFR Library is distributed in the hope that it will be useful, but
15 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
16 or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
17 License for more details.
18 
19 You should have received a copy of the GNU Lesser General Public License
20 along with the GNU MPFR Library; see the file COPYING.LESSER. If not, see
21 https://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc.,
22 51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */
23 
24 #include "mpfr-impl.h"
25 
26 #define mpfr_round_raw_generic mpfr_round_raw
27 #define flag 0
28 #define use_inexp 1
29 #include "round_raw_generic.c"
30 
31 /* mpfr_round_raw_2 is called from mpfr_round_raw2 */
32 #define mpfr_round_raw_generic mpfr_round_raw_2
33 #define flag 1
34 #define use_inexp 0
35 #include "round_raw_generic.c"
36 
37 /* Seems to be unused. Remove comment to implement it.
38 #define mpfr_round_raw_generic mpfr_round_raw_3
39 #define flag 1
40 #define use_inexp 1
41 #include "round_raw_generic.c"
42 */
43 
44 #define mpfr_round_raw_generic mpfr_round_raw_4
45 #define flag 0
46 #define use_inexp 0
47 #include "round_raw_generic.c"
48 
49 /* Note: if the new prec is lower than the current one, a reallocation
50  must not be done (see exp_2.c). */
51 
52 int
54 {
55  mp_limb_t *tmp, *xp;
56  int carry, inexact;
57  mpfr_prec_t nw, ow;
58  MPFR_TMP_DECL(marker);
59 
61 
62  nw = MPFR_PREC2LIMBS (prec); /* needed allocated limbs */
63 
64  /* check if x has enough allocated space for the significand */
65  /* Get the number of limbs from the precision.
66  (Compatible with all allocation methods) */
67  ow = MPFR_LIMB_SIZE (x);
68  if (MPFR_UNLIKELY (nw > ow))
69  {
70  /* FIXME: Variable can't be created using custom allocation,
71  MPFR_DECL_INIT or GROUP_ALLOC: How to detect? */
72  ow = MPFR_GET_ALLOC_SIZE(x);
73  if (nw > ow)
74  {
75  mpfr_size_limb_t *tmpx;
76 
77  /* Realloc significand */
80  MPFR_SET_MANT_PTR(x, tmpx); /* mant ptr must be set
81  before alloc size */
82  MPFR_SET_ALLOC_SIZE(x, nw); /* new number of allocated limbs */
83  }
84  }
85 
87  {
88  MPFR_PREC(x) = prec; /* Special value: need to set prec */
89  if (MPFR_IS_NAN(x))
92  return 0; /* infinity and zero are exact */
93  }
94 
95  /* x is a non-zero real number */
96 
97  MPFR_TMP_MARK(marker);
98  tmp = MPFR_TMP_LIMBS_ALLOC (nw);
99  xp = MPFR_MANT(x);
100  carry = mpfr_round_raw (tmp, xp, MPFR_PREC(x), MPFR_IS_NEG(x),
101  prec, rnd_mode, &inexact);
102  MPFR_PREC(x) = prec;
103 
104  if (MPFR_UNLIKELY(carry))
105  {
106  mpfr_exp_t exp = MPFR_EXP (x);
107 
109  (void) mpfr_overflow(x, rnd_mode, MPFR_SIGN(x));
110  else
111  {
113  MPFR_SET_EXP (x, exp + 1);
114  xp[nw - 1] = MPFR_LIMB_HIGHBIT;
115  if (nw - 1 > 0)
116  MPN_ZERO(xp, nw - 1);
117  }
118  }
119  else
120  MPN_COPY(xp, tmp, nw);
121 
122  MPFR_TMP_FREE(marker);
123  return inexact;
124 }
125 
126 /* assumption: GMP_NUMB_BITS is a power of 2 */
127 
128 /* assuming b is an approximation to x in direction rnd1 with error at
129  most 2^(MPFR_EXP(b)-err), returns 1 if one is able to round exactly
130  x to precision prec with direction rnd2, and 0 otherwise.
131  Side effects: none.
132 
133  rnd1 = RNDN and RNDF are similar: the sign of the error is unknown.
134 
135  rnd2 = RNDF: assume that the user will round the approximation b
136  toward the direction of x, i.e. the opposite of rnd1 in directed
137  rounding modes, otherwise RNDN. Some details:
138 
139  u xinf v xsup w
140  -----|----+----------|--+------------|-----
141  [----- x -----]
142  rnd1 = RNDD b |
143  rnd1 = RNDU b
144 
145  where u, v and w are consecutive machine numbers.
146 
147  * If [xinf,xsup] contains no machine numbers, then return 1.
148 
149  * If [xinf,xsup] contains 2 machine numbers, then return 0.
150 
151  * If [xinf,xsup] contains a single machine number, then return 1 iff
152  the rounding of b is this machine number.
153  With the above choice for the rounding of b, this will always be
154  the case if rnd1 is a directed rounding mode; said otherwise, for
155  rnd2 = RNDF and rnd1 being a directed rounding mode, return 1 iff
156  [xinf,xsup] contains at most 1 machine number.
157 */
158 
159 int
161  mpfr_rnd_t rnd2, mpfr_prec_t prec)
162 {
164  return 0; /* We cannot round if Zero, Nan or Inf */
165  else
167  MPFR_SIGN(b), err, rnd1, rnd2, prec);
168 }
169 
170 /* TODO: mpfr_can_round_raw currently does a memory allocation and some
171  mpn operations. A bit inspection like for mpfr_round_p (round_p.c) may
172  be sufficient, though this would be more complex than the one done in
173  mpfr_round_p, and in particular, for some rnd1/rnd2 combinations, one
174  needs to take care of changes of binade when the value is close to a
175  power of 2. */
176 
177 int
179  mpfr_rnd_t rnd1, mpfr_rnd_t rnd2, mpfr_prec_t prec)
180 {
181  mpfr_prec_t prec2;
182  mp_size_t k, k1, tn;
183  int s, s1;
184  mp_limb_t cc, cc2;
185  mp_limb_t *tmp;
186  mp_limb_t cy = 0, tmp_hi;
187  int res;
188  MPFR_TMP_DECL(marker);
189 
190  /* Since mpfr_can_round is a function in the API, use MPFR_ASSERTN.
191  The specification makes sense only for prec >= 1. */
192  MPFR_ASSERTN (prec >= 1);
193 
194  MPFR_ASSERTD(bp[bn - 1] & MPFR_LIMB_HIGHBIT);
195 
196  MPFR_ASSERT_SIGN(neg);
197  neg = MPFR_IS_NEG_SIGN(neg);
198  MPFR_ASSERTD (neg == 0 || neg == 1);
199 
200  /* For rnd1 and rnd2, transform RNDF / RNDD / RNDU to RNDN / RNDZ / RNDA
201  (with a special case for rnd1 directed rounding, rnd2 = RNDF). */
202 
203  if (rnd1 == MPFR_RNDF)
204  rnd1 = MPFR_RNDN; /* transform RNDF to RNDN */
205  else if (rnd1 != MPFR_RNDN)
206  rnd1 = MPFR_IS_LIKE_RNDZ(rnd1, neg) ? MPFR_RNDZ : MPFR_RNDA;
207 
208  MPFR_ASSERTD (rnd1 == MPFR_RNDN ||
209  rnd1 == MPFR_RNDZ ||
210  rnd1 == MPFR_RNDA);
211 
212  if (rnd2 == MPFR_RNDF)
213  {
214  if (rnd1 == MPFR_RNDN)
215  rnd2 = MPFR_RNDN;
216  else
217  {
218  rnd2 = MPFR_IS_LIKE_RNDZ(rnd1, neg) ? MPFR_RNDA : MPFR_RNDZ;
219  /* Warning: in this case (rnd1 directed rounding, rnd2 = RNDF),
220  the specification of mpfr_can_round says that we should
221  return non-zero (i.e., we can round) when {bp, bn} is
222  exactly representable in precision prec. */
223  if (mpfr_round_raw2 (bp, bn, neg, MPFR_RNDA, prec) == 0)
224  return 1;
225  }
226  }
227  else if (rnd2 != MPFR_RNDN)
228  rnd2 = MPFR_IS_LIKE_RNDZ(rnd2, neg) ? MPFR_RNDZ : MPFR_RNDA;
229 
230  MPFR_ASSERTD (rnd2 == MPFR_RNDN ||
231  rnd2 == MPFR_RNDZ ||
232  rnd2 == MPFR_RNDA);
233 
234  /* For err < prec (+1 for rnd1=RNDN), we can never round correctly, since
235  the error is at least 2*ulp(b) >= ulp(round(b)).
236  However for err = prec (+1 for rnd1=RNDN), we can round correctly in some
237  rare cases where ulp(b) = 1/2*ulp(U) [see below for the definition of U],
238  which implies rnd1 = RNDZ or RNDN, and rnd2 = RNDA or RNDN. */
239 
240  if (MPFR_UNLIKELY (err < prec + (rnd1 == MPFR_RNDN) ||
241  (err == prec + (rnd1 == MPFR_RNDN) &&
242  (rnd1 == MPFR_RNDA ||
243  rnd2 == MPFR_RNDZ))))
244  return 0; /* can't round */
245 
246  /* As a consequence... */
247  MPFR_ASSERTD (err >= prec);
248 
249  /* The bound c on the error |x-b| is: c = 2^(MPFR_EXP(b)-err) <= b/2.
250  * So, we now know that x and b have the same sign. By symmetry,
251  * assume x > 0 and b > 0. We have: L <= x <= U, where, depending
252  * on rnd1:
253  * MPFR_RNDN: L = b-c, U = b+c
254  * MPFR_RNDZ: L = b, U = b+c
255  * MPFR_RNDA: L = b-c, U = b
256  *
257  * We can round x iff round(L,prec,rnd2) = round(U,prec,rnd2).
258  */
259 
260  if (MPFR_UNLIKELY (prec > (mpfr_prec_t) bn * GMP_NUMB_BITS))
261  { /* Then prec > PREC(b): we can round:
262  (i) in rounding to the nearest as long as err >= prec + 2.
263  When err = prec + 1 and b is not a power
264  of two (so that a change of binade cannot occur), then one
265  can round to nearest thanks to the even rounding rule (in the
266  target precision prec, the significand of b ends with a 0).
267  When err = prec + 1 and b is a power of two, when rnd1 = RNDZ one
268  can round too.
269  (ii) in directed rounding mode iff rnd1 is compatible with rnd2
270  and err >= prec + 1, unless b = 2^k and rnd1 = RNDA or RNDN in
271  which case we need err >= prec + 2.
272  */
273  if ((rnd1 == rnd2 || rnd2 == MPFR_RNDN) && err >= prec + 1)
274  {
275  if (rnd1 != MPFR_RNDZ &&
276  err == prec + 1 &&
277  mpfr_powerof2_raw2 (bp, bn))
278  return 0;
279  else
280  return 1;
281  }
282  return 0;
283  }
284 
285  /* now prec <= bn * GMP_NUMB_BITS */
286 
288  {
289  /* we distinguish the case where b is a power of two:
290  rnd1 rnd2 can round?
291  RNDZ RNDZ ok
292  RNDZ RNDA no
293  RNDZ RNDN ok
294  RNDA RNDZ no
295  RNDA RNDA ok except when err = prec + 1
296  RNDA RNDN ok except when err = prec + 1
297  RNDN RNDZ no
298  RNDN RNDA no
299  RNDN RNDN ok except when err = prec + 1 */
300  if (mpfr_powerof2_raw2 (bp, bn))
301  {
302  if ((rnd2 == MPFR_RNDZ || rnd2 == MPFR_RNDA) && rnd1 != rnd2)
303  return 0;
304  else if (rnd1 == MPFR_RNDZ)
305  return 1; /* RNDZ RNDZ and RNDZ RNDN */
306  else
307  return err > prec + 1;
308  }
309 
310  /* now the general case where b is not a power of two:
311  rnd1 rnd2 can round?
312  RNDZ RNDZ ok
313  RNDZ RNDA except when b is representable in precision 'prec'
314  RNDZ RNDN except when b is the middle of two representable numbers in
315  precision 'prec' and b ends with 'xxx0[1]',
316  or b is representable in precision 'prec'
317  and err = prec + 1 and b ends with '1'.
318  RNDA RNDZ except when b is representable in precision 'prec'
319  RNDA RNDA ok
320  RNDA RNDN except when b is the middle of two representable numbers in
321  precision 'prec' and b ends with 'xxx1[1]',
322  or b is representable in precision 'prec'
323  and err = prec + 1 and b ends with '1'.
324  RNDN RNDZ except when b is representable in precision 'prec'
325  RNDN RNDA except when b is representable in precision 'prec'
326  RNDN RNDN except when b is the middle of two representable numbers in
327  precision 'prec', or b is representable in precision 'prec'
328  and err = prec + 1 and b ends with '1'. */
329  if (rnd2 == MPFR_RNDN)
330  {
331  if (err == prec + 1 && (bp[0] & 1))
332  return 0; /* err == prec + 1 implies prec = bn * GMP_NUMB_BITS */
333  if (prec < (mpfr_prec_t) bn * GMP_NUMB_BITS)
334  {
335  k1 = MPFR_PREC2LIMBS (prec + 1);
336  MPFR_UNSIGNED_MINUS_MODULO(s1, prec + 1);
337  if (((bp[bn - k1] >> s1) & 1) &&
338  mpfr_round_raw2 (bp, bn, neg, MPFR_RNDA, prec + 1) == 0)
339  { /* b is the middle of two representable numbers */
340  if (rnd1 == MPFR_RNDN)
341  return 0;
342  k1 = MPFR_PREC2LIMBS (prec);
344  return (rnd1 == MPFR_RNDZ) ^
345  (((bp[bn - k1] >> s1) & 1) == 0);
346  }
347  }
348  return 1;
349  }
350  else if (rnd1 == rnd2) /* cases RNDZ RNDZ or RNDA RNDA: ok */
351  return 1;
352  else
353  return mpfr_round_raw2 (bp, bn, neg, MPFR_RNDA, prec) != 0;
354  }
355 
356  /* now err <= bn * GMP_NUMB_BITS */
357 
358  /* warning: if k = m*GMP_NUMB_BITS, consider limb m-1 and not m */
359  k = (err - 1) / GMP_NUMB_BITS;
361  /* the error corresponds to bit s in limb k, the most significant limb
362  being limb 0; in memory, limb k is bp[bn-1-k]. */
363 
364  k1 = (prec - 1) / GMP_NUMB_BITS;
366  /* the least significant bit is bit s1 in limb k1 */
367 
368  /* We don't need to consider the k1 most significant limbs.
369  They will be considered later only to detect when subtracting
370  the error bound yields a change of binade.
371  Warning! The number with updated bn may no longer be normalized. */
372  k -= k1;
373  bn -= k1;
374  prec2 = prec - (mpfr_prec_t) k1 * GMP_NUMB_BITS;
375 
376  /* We can decide of the correct rounding if rnd2(b-eps) and rnd2(b+eps)
377  give the same result to the target precision 'prec', i.e., if when
378  adding or subtracting (1 << s) in bp[bn-1-k], it does not change the
379  rounding in direction 'rnd2' at ulp-position bp[bn-1] >> s1, taking also
380  into account the possible change of binade. */
381  MPFR_TMP_MARK(marker);
382  tn = bn;
383  k++; /* since we work with k+1 everywhere */
384  tmp = MPFR_TMP_LIMBS_ALLOC (tn);
385  if (bn > k)
386  MPN_COPY (tmp, bp, bn - k); /* copy low bn-k limbs of b into tmp */
387 
388  MPFR_ASSERTD (k > 0);
389 
390  switch (rnd1)
391  {
392  case MPFR_RNDZ:
393  /* rnd1 = Round to Zero */
394  cc = (bp[bn - 1] >> s1) & 1; /* cc is the least significant bit of b */
395  /* mpfr_round_raw2 returns 1 if one should add 1 at ulp(b,prec),
396  and 0 otherwise */
397  cc ^= mpfr_round_raw2 (bp, bn, neg, rnd2, prec2);
398  /* cc is the new value of bit s1 in bp[bn-1] after rounding 'rnd2' */
399 
400  /* now round b + 2^(MPFR_EXP(b)-err) */
401  cy = mpn_add_1 (tmp + bn - k, bp + bn - k, k, MPFR_LIMB_ONE << s);
402  /* propagate carry up to most significant limb */
403  for (tn = 0; tn + 1 < k1 && cy != 0; tn ++)
404  cy = bp[bn + tn] == MPFR_LIMB_MAX;
405  if (cy == 0 && err == prec)
406  {
407  res = 0;
408  goto end;
409  }
410  if (MPFR_UNLIKELY(cy))
411  {
412  /* when a carry occurs, we have b < 2^h <= b+c, we can round iff:
413  rnd2 = RNDZ: never, since b and b+c round to different values;
414  rnd2 = RNDA: when b+c is an exact power of two, and err > prec
415  (since for err = prec, b = 2^h - 1/2*ulp(2^h) is
416  exactly representable and thus rounds to itself);
417  rnd2 = RNDN: whenever cc = 0, since err >= prec implies
418  c <= ulp(b) = 1/2*ulp(2^h), thus b+c rounds to 2^h,
419  and b+c >= 2^h implies that bit 'prec' of b is 1,
420  thus cc = 0 means that b is rounded to 2^h too. */
421  res = (rnd2 == MPFR_RNDZ) ? 0
422  : (rnd2 == MPFR_RNDA) ? (err > prec && k == bn && tmp[0] == 0)
423  : cc == 0;
424  goto end;
425  }
426  break;
427  case MPFR_RNDN:
428  /* rnd1 = Round to nearest */
429 
430  /* first round b+2^(MPFR_EXP(b)-err) */
431  cy = mpn_add_1 (tmp + bn - k, bp + bn - k, k, MPFR_LIMB_ONE << s);
432  /* propagate carry up to most significant limb */
433  for (tn = 0; tn + 1 < k1 && cy != 0; tn ++)
434  cy = bp[bn + tn] == MPFR_LIMB_MAX;
435  cc = (tmp[bn - 1] >> s1) & 1; /* gives 0 when cc=1 */
436  cc ^= mpfr_round_raw2 (tmp, bn, neg, rnd2, prec2);
437  /* cc is the new value of bit s1 in bp[bn-1]+eps after rounding 'rnd2' */
438  if (MPFR_UNLIKELY (cy != 0))
439  {
440  /* when a carry occurs, we have b-c < b < 2^h <= b+c, we can round
441  iff:
442  rnd2 = RNDZ: never, since b-c and b+c round to different values;
443  rnd2 = RNDA: when b+c is an exact power of two, and
444  err > prec + 1 (since for err <= prec + 1,
445  b-c <= 2^h - 1/2*ulp(2^h) is exactly representable
446  and thus rounds to itself);
447  rnd2 = RNDN: whenever err > prec + 1, since for err = prec + 1,
448  b+c rounds to 2^h, and b-c rounds to nextbelow(2^h).
449  For err > prec + 1, c <= 1/4*ulp(b) <= 1/8*ulp(2^h),
450  thus
451  2^h - 1/4*ulp(b) <= b-c < b+c <= 2^h + 1/8*ulp(2^h),
452  therefore both b-c and b+c round to 2^h. */
453  res = (rnd2 == MPFR_RNDZ) ? 0
454  : (rnd2 == MPFR_RNDA) ? (err > prec + 1 && k == bn && tmp[0] == 0)
455  : err > prec + 1;
456  goto end;
457  }
458  subtract_eps:
459  /* now round b-2^(MPFR_EXP(b)-err), this happens for
460  rnd1 = RNDN or RNDA */
461  MPFR_ASSERTD(rnd1 == MPFR_RNDN || rnd1 == MPFR_RNDA);
462  cy = mpn_sub_1 (tmp + bn - k, bp + bn - k, k, MPFR_LIMB_ONE << s);
463  /* propagate the potential borrow up to the most significant limb
464  (it cannot propagate further since the most significant limb is
465  at least MPFR_LIMB_HIGHBIT).
466  Note: we use the same limb tmp[bn-1] to subtract. */
467  tmp_hi = tmp[bn - 1];
468  for (tn = 0; tn < k1 && cy != 0; tn ++)
469  cy = mpn_sub_1 (&tmp_hi, bp + bn + tn, 1, cy);
470  /* We have an exponent decrease when tn = k1 and
471  tmp[bn-1] < MPFR_LIMB_HIGHBIT:
472  b-c < 2^h <= b (for RNDA) or b+c (for RNDN).
473  Then we surely cannot round when rnd2 = RNDZ, since b or b+c round to
474  a value >= 2^h, and b-c rounds to a value < 2^h.
475  We also surely cannot round when (rnd1,rnd2) = (RNDN,RNDA), since
476  b-c rounds to a value <= 2^h, and b+c > 2^h rounds to a value > 2^h.
477  It thus remains:
478  (rnd1,rnd2) = (RNDA,RNDA), (RNDA,RNDN) and (RNDN,RNDN).
479  For (RNDA,RNDA) we can round only when b-c and b round to 2^h, which
480  implies b = 2^h and err > prec (which is true in that case):
481  a necessary condition is that cc = 0.
482  For (RNDA,RNDN) we can round only when b-c and b round to 2^h, which
483  implies b-c >= 2^h - 1/4*ulp(2^h), and b <= 2^h + 1/2*ulp(2^h);
484  since ulp(2^h) = ulp(b), this implies c <= 3/4*ulp(b), thus
485  err > prec.
486  For (RNDN,RNDN) we can round only when b-c and b+c round to 2^h,
487  which implies b-c >= 2^h - 1/4*ulp(2^h), and
488  b+c <= 2^h + 1/2*ulp(2^h);
489  since ulp(2^h) = ulp(b), this implies 2*c <= 3/4*ulp(b), thus
490  err > prec+1.
491  */
492  if (tn == k1 && tmp_hi < MPFR_LIMB_HIGHBIT) /* exponent decrease */
493  {
494  if (rnd2 == MPFR_RNDZ || (rnd1 == MPFR_RNDN && rnd2 == MPFR_RNDA) ||
495  cc != 0 /* b or b+c does not round to 2^h */)
496  {
497  res = 0;
498  goto end;
499  }
500  /* in that case since the most significant bit of tmp is 0, we
501  should consider one more bit; res = 0 when b-c does not round
502  to 2^h. */
503  res = mpfr_round_raw2 (tmp, bn, neg, rnd2, prec2 + 1) != 0;
504  goto end;
505  }
506  if (err == prec + (rnd1 == MPFR_RNDN))
507  {
508  /* No exponent increase nor decrease, thus we have |U-L| = ulp(b).
509  For rnd2 = RNDZ or RNDA, either [L,U] contains one representable
510  number in the target precision, and then L and U round
511  differently; or both L and U are representable: they round
512  differently too; thus in all cases we cannot round.
513  For rnd2 = RNDN, the only case where we can round is when the
514  middle of [L,U] (i.e. b) is representable, and ends with a 0. */
515  res = (rnd2 == MPFR_RNDN && (((bp[bn - 1] >> s1) & 1) == 0) &&
516  mpfr_round_raw2 (bp, bn, neg, MPFR_RNDZ, prec2) ==
517  mpfr_round_raw2 (bp, bn, neg, MPFR_RNDA, prec2));
518  goto end;
519  }
520  break;
521  default:
522  /* rnd1 = Round away */
523  MPFR_ASSERTD (rnd1 == MPFR_RNDA);
524  cc = (bp[bn - 1] >> s1) & 1;
525  /* the mpfr_round_raw2() call below returns whether one should add 1 or
526  not for rounding */
527  cc ^= mpfr_round_raw2 (bp, bn, neg, rnd2, prec2);
528  /* cc is the new value of bit s1 in bp[bn-1]+eps after rounding 'rnd2' */
529 
530  goto subtract_eps;
531  }
532 
533  cc2 = (tmp[bn - 1] >> s1) & 1;
534  res = cc == (cc2 ^ mpfr_round_raw2 (tmp, bn, neg, rnd2, prec2));
535 
536  end:
537  MPFR_TMP_FREE(marker);
538  return res;
539 }
double __cdecl exp(double _X)
bp
Definition: action.c:1035
Definition: asl.h:63
#define b
Definition: jpegint.h:372
mpfr_exp_t __gmpfr_emax
Definition: exceptions.c:27
int mpfr_overflow(mpfr_ptr x, mpfr_rnd_t rnd_mode, int sign)
Definition: exceptions.c:406
static void
Definition: fpif.c:118
#define xp
#define s
Definition: afcover.h:80
#define MPN_COPY(d, s, n)
Definition: gmp-impl.h:1849
#define MPN_ZERO(dst, n)
Definition: gmp-impl.h:1919
#define mpn_add_1
Definition: gmp.h:1468
#define GMP_NUMB_BITS
Definition: gmp.h:46
#define mpn_sub_1
Definition: gmp.h:1608
long int mp_size_t
Definition: gmp.h:175
#define nw
Definition: gsftopk.c:503
int int cy
Definition: gdfx.h:13
void * mpfr_reallocate_func(void *ptr, size_t old_size, size_t new_size)
Definition: mpfr-gmp.c:319
#define MPFR_IS_INF(x)
Definition: mpfr-impl.h:1082
#define MPFR_SET_EXP(x, e)
Definition: mpfr-impl.h:1059
#define MPFR_LIMB_HIGHBIT
Definition: mpfr-impl.h:1276
#define MPFR_PREC_COND(p)
Definition: mpfr-impl.h:942
#define MPFR_IS_NEG_SIGN(s1)
Definition: mpfr-impl.h:1154
#define MPFR_IS_LIKE_RNDZ(rnd, neg)
Definition: mpfr-impl.h:1207
#define MPFR_UNLIKELY(x)
Definition: mpfr-impl.h:1490
#define MPFR_IS_NAN(x)
Definition: mpfr-impl.h:1080
#define MPFR_IS_NEG(x)
Definition: mpfr-impl.h:1140
#define MPFR_LIMB_MAX
Definition: mpfr-impl.h:1277
#define MPFR_PREC(x)
Definition: mpfr-impl.h:958
#define mpfr_round_raw2(xp, xn, neg, r, prec)
Definition: mpfr-impl.h:2432
int mpfr_round_raw(mp_limb_t *, const mp_limb_t *, mpfr_prec_t, int, mpfr_prec_t, mpfr_rnd_t, int *)
#define MPFR_ASSERT_SIGN(s)
Definition: mpfr-impl.h:1149
#define MPFR_TMP_FREE
Definition: mpfr-impl.h:1336
#define MPFR_IS_ZERO(x)
Definition: mpfr-impl.h:1084
#define MPFR_SET_ALLOC_SIZE(x, n)
Definition: mpfr-impl.h:1321
#define MPFR_LIMB_SIZE(x)
Definition: mpfr-impl.h:963
#define MPFR_MALLOC_SIZE(s)
Definition: mpfr-impl.h:1323
#define MPFR_GET_ALLOC_SIZE(x)
Definition: mpfr-impl.h:1319
#define MPFR_LIMB_ONE
Definition: mpfr-impl.h:1275
#define MPFR_RET_NAN
Definition: mpfr-impl.h:1184
#define MPFR_TMP_DECL
Definition: mpfr-impl.h:1333
#define MPFR_ASSERTN(expr)
Definition: mpfr-impl.h:495
int mpfr_powerof2_raw2(const mp_limb_t *, mp_size_t)
Definition: powerof2.c:42
#define MPFR_PREC2LIMBS(p)
Definition: mpfr-impl.h:955
#define MPFR_TMP_MARK
Definition: mpfr-impl.h:1334
#define MPFR_ASSERTD(expr)
Definition: mpfr-impl.h:516
#define MPFR_TMP_LIMBS_ALLOC(N)
Definition: mpfr-impl.h:1344
#define MPFR_GET_REAL_PTR(x)
Definition: mpfr-impl.h:1327
#define MPFR_UNSIGNED_MINUS_MODULO(s, a)
Definition: mpfr-impl.h:1603
#define MPFR_EXP(x)
Definition: mpfr-impl.h:959
#define MPFR_IS_SINGULAR(x)
Definition: mpfr-impl.h:1100
#define MPFR_SET_MANT_PTR(x, p)
Definition: mpfr-impl.h:1325
#define MPFR_MANT(x)
Definition: mpfr-impl.h:960
long mpfr_prec_t
Definition: mpfr.h:168
#define MPFR_SIGN(x)
Definition: mpfr.h:260
mpfr_rnd_t
Definition: mpfr.h:102
@ MPFR_RNDA
Definition: mpfr.h:107
@ MPFR_RNDF
Definition: mpfr.h:108
@ MPFR_RNDN
Definition: mpfr.h:103
@ MPFR_RNDZ
Definition: mpfr.h:104
long mpfr_exp_t
Definition: mpfr.h:195
@ err
Definition: mtxline.h:24
float x
Definition: cordic.py:15
int tn
Definition: fc-lang.py:225
int k
Definition: otp-parser.c:70
#define res(length)
Definition: picttoppm.c:287
#define k1
int mpfr_can_round(mpfr_srcptr b, mpfr_exp_t err, mpfr_rnd_t rnd1, mpfr_rnd_t rnd2, mpfr_prec_t prec)
Definition: round_prec.c:160
int mpfr_prec_round(mpfr_ptr x, mpfr_prec_t prec, mpfr_rnd_t rnd_mode)
Definition: round_prec.c:53
int mpfr_can_round_raw(const mp_limb_t *bp, mp_size_t bn, int neg, mpfr_exp_t err, mpfr_rnd_t rnd1, mpfr_rnd_t rnd2, mpfr_prec_t prec)
Definition: round_prec.c:178
Definition: sh2.c:920
s1
Definition: t4ht.c:1059
#define end(cp)
Definition: zic.c:71