1 /* mpfr_round_p -- check if an approximation is roundable.
2
3 Copyright 2005-2023 Free Software Foundation, Inc.
4 Contributed by the AriC and Caramba projects, INRIA.
5
6 This file is part of the GNU MPFR Library.
7
8 The GNU MPFR Library is free software; you can redistribute it and/or modify
9 it under the terms of the GNU Lesser General Public License as published by
10 the Free Software Foundation; either version 3 of the License, or (at your
11 option) any later version.
12
13 The GNU MPFR Library is distributed in the hope that it will be useful, but
14 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
15 or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
16 License for more details.
17
18 You should have received a copy of the GNU Lesser General Public License
19 along with the GNU MPFR Library; see the file COPYING.LESSER. If not, see
20 https://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc.,
21 51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */
22
23 #include "mpfr-impl.h"
24
25 /* Check against mpfr_can_round? */
26 #if MPFR_WANT_ASSERT >= 2
27 int mpfr_round_p_2 (mp_limb_t *, mp_size_t, mpfr_exp_t, mpfr_prec_t);
28 int
29 mpfr_round_p (mp_limb_t *bp, mp_size_t bn, mpfr_exp_t err0, mpfr_prec_t prec)
30 {
31 int i1, i2;
32
33 MPFR_ASSERTN(bp[bn - 1] & MPFR_LIMB_HIGHBIT);
34
35 i1 = mpfr_round_p_2 (bp, bn, err0, prec);
36
37 /* Note: since revision 10747, mpfr_can_round_raw is supposed to be always
38 correct, whereas mpfr_round_p_2 might return 0 in some cases where one
39 could round, for example with err0=67 and prec=54:
40 b = 1111101101010001100011111011100010100011101111011011101111111111
41 thus we cannot compare i1 and i2, we only can check that we don't have
42 i1 <> 0 and i2 = 0.
43 */
44 i2 = mpfr_can_round_raw (bp, bn, MPFR_SIGN_POS, err0,
45 MPFR_RNDN, MPFR_RNDZ, prec);
46 if (i1 && (i2 == 0))
47 {
48 fprintf (stderr, "mpfr_round_p(%d) != mpfr_can_round(%d)!\n"
49 "bn = %lu, err0 = %ld, prec = %lu\nbp = ", i1, i2,
50 (unsigned long) bn, (long) err0, (unsigned long) prec);
51 #ifndef MPFR_USE_MINI_GMP
52 gmp_fprintf (stderr, "%NX\n", bp, bn);
53 #endif
54 MPFR_ASSERTN (0);
55 }
56
57 return i1;
58 }
59 # define mpfr_round_p mpfr_round_p_2
60 #endif /* MPFR_WANT_ASSERT >= 2 */
61
62 /*
63 * Assuming {bp, bn} is an approximation of a non-singular number
64 * with error at most equal to 2^(EXP(b)-err0) (`err0' bits of b are known)
65 * of direction unknown, check if we can round b toward zero with
66 * precision prec.
67 */
68 int
69 mpfr_round_p (mp_limb_t *bp, mp_size_t bn, mpfr_exp_t err0, mpfr_prec_t prec)
70 {
71 mpfr_prec_t err;
72 mp_size_t k, n;
73 mp_limb_t tmp, mask;
74 int s;
75
76 MPFR_ASSERTD(bp[bn - 1] & MPFR_LIMB_HIGHBIT);
77
78 err = (mpfr_prec_t) bn * GMP_NUMB_BITS;
79 if (MPFR_UNLIKELY (err0 <= 0 || (mpfr_uexp_t) err0 <= prec || prec >= err))
80 return 0; /* can't round */
81 err = MIN (err, (mpfr_uexp_t) err0);
82
83 k = prec / GMP_NUMB_BITS;
84 s = GMP_NUMB_BITS - prec % GMP_NUMB_BITS;
85 n = err / GMP_NUMB_BITS - k;
86
87 MPFR_ASSERTD (n >= 0);
88 MPFR_ASSERTD (bn > k);
89
90 /* Check first limb */
91 bp += bn - 1 - k;
92 tmp = *bp--;
93 mask = s == GMP_NUMB_BITS ? MPFR_LIMB_MAX : MPFR_LIMB_MASK (s);
94 tmp &= mask;
95
96 if (MPFR_LIKELY (n == 0))
97 {
98 /* prec and error are in the same limb */
99 s = GMP_NUMB_BITS - err % GMP_NUMB_BITS;
100 MPFR_ASSERTD (s < GMP_NUMB_BITS);
101 tmp >>= s;
102 mask >>= s;
103 return tmp != 0 && tmp != mask;
104 }
105 else if (MPFR_UNLIKELY (tmp == 0))
106 {
107 /* Check if all (n-1) limbs are 0 */
108 while (--n)
109 if (*bp-- != 0)
110 return 1;
111 /* Check if final error limb is 0 */
112 s = GMP_NUMB_BITS - err % GMP_NUMB_BITS;
113 if (s == GMP_NUMB_BITS)
114 return 0;
115 tmp = *bp >> s;
116 return tmp != 0;
117 }
118 else if (MPFR_UNLIKELY (tmp == mask))
119 {
120 /* Check if all (n-1) limbs are 11111111111111111 */
121 while (--n)
122 if (*bp-- != MPFR_LIMB_MAX)
123 return 1;
124 /* Check if final error limb is 0 */
125 s = GMP_NUMB_BITS - err % GMP_NUMB_BITS;
126 if (s == GMP_NUMB_BITS)
127 return 0;
128 tmp = *bp >> s;
129 return tmp != (MPFR_LIMB_MAX >> s);
130 }
131 else
132 {
133 /* First limb is different from 000000 or 1111111 */
134 return 1;
135 }
136 }