summaryrefslogtreecommitdiff
path: root/rint.c
blob: c8f1a072c9e2e42a44cd3430eed6e39d63311da7 (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
/* mpfr_rint -- Round to an integer.

Copyright 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008 Free Software Foundation, Inc.
Contributed by the Arenaire and Cacao projects, INRIA.

This file is part of the MPFR Library.

The MPFR Library is free software; you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation; either version 2.1 of the License, or (at your
option) any later version.

The MPFR Library is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
License for more details.

You should have received a copy of the GNU Lesser General Public License
along with the MPFR Library; see the file COPYING.LIB.  If not, write to
the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston,
MA 02110-1301, USA. */

#include "mpfr-impl.h"

/* Merge the following mpfr_rint code with mpfr_round_raw_generic? */

int
mpfr_rint (mpfr_ptr r, mpfr_srcptr u, mpfr_rnd_t rnd_mode)
{
  int sign;
  int rnd_away;
  mp_exp_t exp;

  if (MPFR_UNLIKELY( MPFR_IS_SINGULAR(u) ))
    {
      if (MPFR_IS_NAN(u))
        {
          MPFR_SET_NAN(r);
          MPFR_RET_NAN;
        }
      MPFR_SET_SAME_SIGN(r, u);
      if (MPFR_IS_INF(u))
        {
          MPFR_SET_INF(r);
          MPFR_RET(0);  /* infinity is exact */
        }
      else /* now u is zero */
        {
          MPFR_ASSERTD(MPFR_IS_ZERO(u));
          MPFR_SET_ZERO(r);
          MPFR_RET(0);  /* zero is exact */
        }
    }
  MPFR_SET_SAME_SIGN (r, u); /* Does nothing if r==u */

  sign = MPFR_INT_SIGN (u);
  exp = MPFR_GET_EXP (u);

  rnd_away =
    rnd_mode == GMP_RNDD ? sign < 0 :
    rnd_mode == GMP_RNDU ? sign > 0 :
    rnd_mode == GMP_RNDZ ? 0 : -1;

  /* rnd_away:
     1 if round away from zero,
     0 if round to zero,
     -1 if not decided yet.
   */

  if (MPFR_UNLIKELY (exp <= 0))  /* 0 < |u| < 1 ==> round |u| to 0 or 1 */
    {
      /* Note: in the GMP_RNDN mode, 0.5 must be rounded to 0. */
      if (rnd_away != 0 &&
          (rnd_away > 0 ||
           (exp == 0 && (rnd_mode == GMP_RNDNA ||
                         !mpfr_powerof2_raw (u)))))
        {
          mp_limb_t *rp;
          mp_size_t rm;

          rp = MPFR_MANT(r);
          rm = (MPFR_PREC(r) - 1) / BITS_PER_MP_LIMB;
          rp[rm] = MPFR_LIMB_HIGHBIT;
          MPN_ZERO(rp, rm);
          MPFR_SET_EXP (r, 1);  /* |r| = 1 */
          MPFR_RET(sign > 0 ? 2 : -2);
        }
      else
        {
          MPFR_SET_ZERO(r);  /* r = 0 */
          MPFR_RET(sign > 0 ? -2 : 2);
        }
    }
  else  /* exp > 0, |u| >= 1 */
    {
      mp_limb_t *up, *rp;
      mp_size_t un, rn, ui;
      int sh, idiff;
      int uflags;

      /*
       * uflags will contain:
       *   _ 0 if u is an integer representable in r,
       *   _ 1 if u is an integer not representable in r,
       *   _ 2 if u is not an integer.
       */

      up = MPFR_MANT(u);
      rp = MPFR_MANT(r);

      un = MPFR_LIMB_SIZE(u);
      rn = MPFR_LIMB_SIZE(r);
      MPFR_UNSIGNED_MINUS_MODULO (sh, MPFR_PREC (r));

      MPFR_SET_EXP (r, exp); /* Does nothing if r==u */

      if ((exp - 1) / BITS_PER_MP_LIMB >= un)
        {
          ui = un;
          idiff = 0;
          uflags = 0;  /* u is an integer, representable or not in r */
        }
      else
        {
          mp_size_t uj;

          ui = (exp - 1) / BITS_PER_MP_LIMB + 1;  /* #limbs of the int part */
          MPFR_ASSERTD (un >= ui);
          uj = un - ui;  /* lowest limb of the integer part */
          idiff = exp % BITS_PER_MP_LIMB;  /* #int-part bits in up[uj] or 0 */

          uflags = idiff == 0 || (up[uj] << idiff) == 0 ? 0 : 2;
          if (uflags == 0)
            while (uj > 0)
              if (up[--uj] != 0)
                {
                  uflags = 2;
                  break;
                }
        }

      if (ui > rn)
        {
          /* More limbs in the integer part of u than in r.
             Just round u with the precision of r. */
          MPFR_ASSERTD (rp != up && un > rn);
          MPN_COPY (rp, up + (un - rn), rn); /* r != u */
          if (rnd_away < 0)
            {
              /* This is a rounding to nearest mode (GMP_RNDN or GMP_RNDNA).
                 Decide the rounding direction here. */
              if (rnd_mode == GMP_RNDN &&
                  (rp[0] & (MPFR_LIMB_ONE << sh)) == 0)
                { /* halfway cases rounded towards zero */
                  mp_limb_t a, b;
                  /* a: rounding bit and some of the following bits */
                  /* b: boundary for a (weight of the rounding bit in a) */
                  if (sh != 0)
                    {
                      a = rp[0] & ((MPFR_LIMB_ONE << sh) - 1);
                      b = MPFR_LIMB_ONE << (sh - 1);
                    }
                  else
                    {
                      a = up[un - rn - 1];
                      b = MPFR_LIMB_HIGHBIT;
                    }
                  rnd_away = a > b;
                  if (a == b)
                    {
                      mp_size_t i;
                      for (i = un - rn - 1 - (sh == 0); i >= 0; i--)
                        if (up[i] != 0)
                          {
                            rnd_away = 1;
                            break;
                          }
                    }
                }
              else  /* halfway cases rounded away from zero */
                rnd_away =  /* rounding bit */
                  ((sh != 0 && (rp[0] & (MPFR_LIMB_ONE << (sh - 1))) != 0) ||
                   (sh == 0 && (up[un - rn - 1] & MPFR_LIMB_HIGHBIT) != 0));
            }
          if (uflags == 0)
            { /* u is an integer; determine if it is representable in r */
              if (sh != 0 && rp[0] << (BITS_PER_MP_LIMB - sh) != 0)
                uflags = 1;  /* u is not representable in r */
              else
                {
                  mp_size_t i;
                  for (i = un - rn - 1; i >= 0; i--)
                    if (up[i] != 0)
                      {
                        uflags = 1;  /* u is not representable in r */
                        break;
                      }
                }
            }
        }
      else  /* ui <= rn */
        {
          mp_size_t uj, rj;
          int ush;

          uj = un - ui;  /* lowest limb of the integer part in u */
          rj = rn - ui;  /* lowest limb of the integer part in r */

          if (MPFR_LIKELY (rp != up))
            MPN_COPY(rp + rj, up + uj, ui);

          /* Ignore the lowest rj limbs, all equal to zero. */
          rp += rj;
          rn = ui;

          /* number of fractional bits in whole rp[0] */
          ush = idiff == 0 ? 0 : BITS_PER_MP_LIMB - idiff;

          if (rj == 0 && ush < sh)
            {
              /* If u is an integer (uflags == 0), we need to determine
                 if it is representable in r, i.e. if its sh - ush bits
                 in the non-significant part of r are all 0. */
              if (uflags == 0 && (rp[0] & ((MPFR_LIMB_ONE << sh) -
                                           (MPFR_LIMB_ONE << ush))) != 0)
                uflags = 1;  /* u is an integer not representable in r */
            }
          else  /* The integer part of u fits in r, we'll round to it. */
            sh = ush;

          if (rnd_away < 0)
            {
              /* This is a rounding to nearest mode.
                 Decide the rounding direction here. */
              if (uj == 0 && sh == 0)
                rnd_away = 0; /* rounding bit = 0 (not represented in u) */
              else if (rnd_mode == GMP_RNDN &&
                       (rp[0] & (MPFR_LIMB_ONE << sh)) == 0)
                { /* halfway cases rounded towards zero */
                  mp_limb_t a, b;
                  /* a: rounding bit and some of the following bits */
                  /* b: boundary for a (weight of the rounding bit in a) */
                  if (sh != 0)
                    {
                      a = rp[0] & ((MPFR_LIMB_ONE << sh) - 1);
                      b = MPFR_LIMB_ONE << (sh - 1);
                    }
                  else
                    {
                      MPFR_ASSERTD (uj >= 1);  /* see above */
                      a = up[uj - 1];
                      b = MPFR_LIMB_HIGHBIT;
                    }
                  rnd_away = a > b;
                  if (a == b)
                    {
                      mp_size_t i;
                      for (i = uj - 1 - (sh == 0); i >= 0; i--)
                        if (up[i] != 0)
                          {
                            rnd_away = 1;
                            break;
                          }
                    }
                }
              else  /* halfway cases rounded away from zero */
                rnd_away =  /* rounding bit */
                  ((sh != 0 && (rp[0] & (MPFR_LIMB_ONE << (sh - 1))) != 0) ||
                   (sh == 0 && (MPFR_ASSERTD (uj >= 1),
                                up[uj - 1] & MPFR_LIMB_HIGHBIT) != 0));
            }
          /* Now we can make the low rj limbs to 0 */
          MPN_ZERO (rp-rj, rj);
        }

      if (sh != 0)
        rp[0] &= MP_LIMB_T_MAX << sh;

      /* If u is a representable integer, there is no rounding. */
      if (uflags == 0)
        MPFR_RET(0);

      MPFR_ASSERTD (rnd_away >= 0);  /* rounding direction is defined */
      if (rnd_away && mpn_add_1(rp, rp, rn, MPFR_LIMB_ONE << sh))
        {
          if (exp == __gmpfr_emax)
            return mpfr_overflow(r, rnd_mode, MPFR_SIGN(r)) >= 0 ?
              uflags : -uflags;
          else
            {
              MPFR_SET_EXP(r, exp + 1);
              rp[rn-1] = MPFR_LIMB_HIGHBIT;
            }
        }

      MPFR_RET (rnd_away ^ (sign < 0) ? uflags : -uflags);
    }  /* exp > 0, |u| >= 1 */
}

#undef mpfr_round

int
mpfr_round (mpfr_ptr r, mpfr_srcptr u)
{
  return mpfr_rint(r, u, GMP_RNDNA);
}

#undef mpfr_trunc

int
mpfr_trunc (mpfr_ptr r, mpfr_srcptr u)
{
  return mpfr_rint(r, u, GMP_RNDZ);
}

#undef mpfr_ceil

int
mpfr_ceil (mpfr_ptr r, mpfr_srcptr u)
{
  return mpfr_rint(r, u, GMP_RNDU);
}

#undef mpfr_floor

int
mpfr_floor (mpfr_ptr r, mpfr_srcptr u)
{
  return mpfr_rint(r, u, GMP_RNDD);
}

#undef mpfr_rint_round

int
mpfr_rint_round (mpfr_ptr r, mpfr_srcptr u, mpfr_rnd_t rnd_mode)
{
  if (MPFR_UNLIKELY( MPFR_IS_SINGULAR(u) ) || mpfr_integer_p (u))
    return mpfr_set (r, u, rnd_mode);
  else
    {
      mpfr_t tmp;
      int inex;
      MPFR_SAVE_EXPO_DECL (expo);
      MPFR_BLOCK_DECL (flags);

      MPFR_SAVE_EXPO_MARK (expo);
      mpfr_init2 (tmp, MPFR_PREC (u));
      /* round(u) is representable in tmp unless an overflow occurs */
      MPFR_BLOCK (flags, mpfr_round (tmp, u));
      inex = (MPFR_OVERFLOW (flags)
              ? mpfr_overflow (r, rnd_mode, MPFR_SIGN (u))
              : mpfr_set (r, tmp, rnd_mode));
      mpfr_clear (tmp);
      MPFR_SAVE_EXPO_FREE (expo);
      return mpfr_check_range (r, inex, rnd_mode);
    }
}

#undef mpfr_rint_trunc

int
mpfr_rint_trunc (mpfr_ptr r, mpfr_srcptr u, mpfr_rnd_t rnd_mode)
{
  if (MPFR_UNLIKELY( MPFR_IS_SINGULAR(u) ) || mpfr_integer_p (u))
    return mpfr_set (r, u, rnd_mode);
  else
    {
      mpfr_t tmp;
      int inex;
      MPFR_SAVE_EXPO_DECL (expo);

      MPFR_SAVE_EXPO_MARK (expo);
      mpfr_init2 (tmp, MPFR_PREC (u));
      /* trunc(u) is always representable in tmp */
      mpfr_trunc (tmp, u);
      inex = mpfr_set (r, tmp, rnd_mode);
      mpfr_clear (tmp);
      MPFR_SAVE_EXPO_FREE (expo);
      return mpfr_check_range (r, inex, rnd_mode);
    }
}

#undef mpfr_rint_ceil

int
mpfr_rint_ceil (mpfr_ptr r, mpfr_srcptr u, mpfr_rnd_t rnd_mode)
{
  if (MPFR_UNLIKELY( MPFR_IS_SINGULAR(u) ) || mpfr_integer_p (u))
    return mpfr_set (r, u, rnd_mode);
  else
    {
      mpfr_t tmp;
      int inex;
      MPFR_SAVE_EXPO_DECL (expo);
      MPFR_BLOCK_DECL (flags);

      MPFR_SAVE_EXPO_MARK (expo);
      mpfr_init2 (tmp, MPFR_PREC (u));
      /* ceil(u) is representable in tmp unless an overflow occurs */
      MPFR_BLOCK (flags, mpfr_ceil (tmp, u));
      inex = (MPFR_OVERFLOW (flags)
              ? mpfr_overflow (r, rnd_mode, MPFR_SIGN_POS)
              : mpfr_set (r, tmp, rnd_mode));
      mpfr_clear (tmp);
      MPFR_SAVE_EXPO_FREE (expo);
      return mpfr_check_range (r, inex, rnd_mode);
    }
}

#undef mpfr_rint_floor

int
mpfr_rint_floor (mpfr_ptr r, mpfr_srcptr u, mpfr_rnd_t rnd_mode)
{
  if (MPFR_UNLIKELY( MPFR_IS_SINGULAR(u) ) || mpfr_integer_p (u))
    return mpfr_set (r, u, rnd_mode);
  else
    {
      mpfr_t tmp;
      int inex;
      MPFR_SAVE_EXPO_DECL (expo);
      MPFR_BLOCK_DECL (flags);

      MPFR_SAVE_EXPO_MARK (expo);
      mpfr_init2 (tmp, MPFR_PREC (u));
      /* floor(u) is representable in tmp unless an overflow occurs */
      MPFR_BLOCK (flags, mpfr_floor (tmp, u));
      inex = (MPFR_OVERFLOW (flags)
              ? mpfr_overflow (r, rnd_mode, MPFR_SIGN_NEG)
              : mpfr_set (r, tmp, rnd_mode));
      mpfr_clear (tmp);
      MPFR_SAVE_EXPO_FREE (expo);
      return mpfr_check_range (r, inex, rnd_mode);
    }
}