1 /* mpfr_nextabove, mpfr_nextbelow, mpfr_nexttoward -- next representable
2 floating-point number
3
4 Copyright 1999, 2001-2020 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 /* Note concerning the exceptions: In case of NaN result, the NaN flag is
25 * set as usual. No underflow or overflow is generated (this contradicts
26 * the obsolete IEEE 754-1985 standard for Nextafter, but conforms to the
27 * current standard IEEE 754-2008 for nextUp and nextDown).
28 */
29
30 #include "mpfr-impl.h"
31
32 void
mpfr_nexttozero(mpfr_ptr x)33 mpfr_nexttozero (mpfr_ptr x)
34 {
35 if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
36 {
37 if (MPFR_IS_INF (x))
38 {
39 mpfr_setmax (x, __gmpfr_emax);
40 }
41 else
42 {
43 MPFR_ASSERTN (MPFR_IS_ZERO (x));
44 MPFR_CHANGE_SIGN(x);
45 mpfr_setmin (x, __gmpfr_emin);
46 }
47 }
48 else
49 {
50 mp_size_t xn;
51 int sh;
52 mp_limb_t *xp;
53
54 xn = MPFR_LIMB_SIZE (x);
55 MPFR_UNSIGNED_MINUS_MODULO (sh, MPFR_PREC(x));
56 xp = MPFR_MANT(x);
57 mpn_sub_1 (xp, xp, xn, MPFR_LIMB_ONE << sh);
58 if (MPFR_UNLIKELY (MPFR_LIMB_MSB (xp[xn-1]) == 0))
59 { /* was an exact power of two: not normalized any more,
60 thus do not use MPFR_GET_EXP. */
61 mpfr_exp_t exp = MPFR_EXP (x);
62 if (MPFR_UNLIKELY (exp == __gmpfr_emin))
63 MPFR_SET_ZERO(x);
64 else
65 {
66 MPFR_SET_EXP (x, exp - 1);
67 /* The following is valid whether xn = 1 or xn > 1. */
68 xp[xn-1] |= MPFR_LIMB_HIGHBIT;
69 }
70 }
71 }
72 }
73
74 void
mpfr_nexttoinf(mpfr_ptr x)75 mpfr_nexttoinf (mpfr_ptr x)
76 {
77 if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
78 {
79 if (MPFR_IS_ZERO (x))
80 mpfr_setmin (x, __gmpfr_emin);
81 }
82 else
83 {
84 mp_size_t xn;
85 int sh;
86 mp_limb_t *xp;
87
88 xn = MPFR_LIMB_SIZE (x);
89 MPFR_UNSIGNED_MINUS_MODULO (sh, MPFR_PREC(x));
90 xp = MPFR_MANT(x);
91 if (MPFR_UNLIKELY (mpn_add_1 (xp, xp, xn, MPFR_LIMB_ONE << sh)))
92 /* got 1.0000... */
93 {
94 mpfr_exp_t exp = MPFR_EXP (x);
95 if (MPFR_UNLIKELY (exp == __gmpfr_emax))
96 MPFR_SET_INF (x);
97 else
98 {
99 MPFR_SET_EXP (x, exp + 1);
100 xp[xn-1] = MPFR_LIMB_HIGHBIT;
101 }
102 }
103 }
104 }
105
106 void
mpfr_nextabove(mpfr_ptr x)107 mpfr_nextabove (mpfr_ptr x)
108 {
109 if (MPFR_UNLIKELY(MPFR_IS_NAN(x)))
110 {
111 __gmpfr_flags |= MPFR_FLAGS_NAN;
112 return;
113 }
114 if (MPFR_IS_NEG(x))
115 mpfr_nexttozero (x);
116 else
117 mpfr_nexttoinf (x);
118 }
119
120 void
mpfr_nextbelow(mpfr_ptr x)121 mpfr_nextbelow (mpfr_ptr x)
122 {
123 if (MPFR_UNLIKELY(MPFR_IS_NAN(x)))
124 {
125 __gmpfr_flags |= MPFR_FLAGS_NAN;
126 return;
127 }
128
129 if (MPFR_IS_NEG(x))
130 mpfr_nexttoinf (x);
131 else
132 mpfr_nexttozero (x);
133 }
134
135 void
mpfr_nexttoward(mpfr_ptr x,mpfr_srcptr y)136 mpfr_nexttoward (mpfr_ptr x, mpfr_srcptr y)
137 {
138 int s;
139
140 if (MPFR_UNLIKELY(MPFR_IS_NAN(x)))
141 {
142 __gmpfr_flags |= MPFR_FLAGS_NAN;
143 return;
144 }
145 else if (MPFR_UNLIKELY(MPFR_IS_NAN(x) || MPFR_IS_NAN(y)))
146 {
147 MPFR_SET_NAN(x);
148 __gmpfr_flags |= MPFR_FLAGS_NAN;
149 return;
150 }
151
152 s = mpfr_cmp (x, y);
153 if (s == 0)
154 return;
155 else if (s < 0)
156 mpfr_nextabove (x);
157 else
158 mpfr_nextbelow (x);
159 }
160