1 /* mpfr_frac -- Fractional part of a floating-point number.
2
3 Copyright 2002-2004, 2006-2023 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
24 #define MPFR_NEED_LONGLONG_H
25 #include "mpfr-impl.h"
26
27 /* Optimization note: it is not a good idea to call mpfr_integer_p,
28 as some cases will take longer (the number may be parsed twice). */
29
30 int
31 mpfr_frac (mpfr_ptr r, mpfr_srcptr u, mpfr_rnd_t rnd_mode)
32 {
33 mpfr_exp_t re, ue;
34 mpfr_prec_t uq;
35 mp_size_t un, tn, t0;
36 mp_limb_t *up, *tp, k;
37 int sh;
38 mpfr_t tmp;
39 mpfr_ptr t;
40 int inex;
41 MPFR_SAVE_EXPO_DECL (expo);
42
43 /* Special cases */
44 if (MPFR_UNLIKELY(MPFR_IS_NAN(u)))
45 {
46 MPFR_SET_NAN(r);
47 MPFR_RET_NAN;
48 }
49 else if (MPFR_UNLIKELY(MPFR_IS_INF(u) || mpfr_integer_p (u)))
50 {
51 MPFR_SET_SAME_SIGN(r, u);
52 MPFR_SET_ZERO(r);
53 MPFR_RET(0); /* zero is exact */
54 }
55
56 ue = MPFR_GET_EXP (u);
57 if (ue <= 0) /* |u| < 1 */
58 return mpfr_set (r, u, rnd_mode);
59
60 /* Now |u| >= 1, meaning that an overflow is not possible. */
61
62 uq = MPFR_PREC(u);
63 un = (uq - 1) / GMP_NUMB_BITS; /* index of most significant limb */
64 un -= (mp_size_t) (ue / GMP_NUMB_BITS);
65 /* now the index of the MSL containing bits of the fractional part */
66
67 up = MPFR_MANT(u);
68 sh = ue % GMP_NUMB_BITS;
69 k = up[un] << sh;
70 /* the first bit of the fractional part is the MSB of k */
71
72 if (k != 0)
73 {
74 int cnt;
75
76 count_leading_zeros(cnt, k);
77 /* first bit 1 of the fractional part -> MSB of the number */
78 re = -cnt;
79 sh += cnt;
80 MPFR_ASSERTN (sh < GMP_NUMB_BITS);
81 k <<= cnt;
82 }
83 else
84 {
85 re = sh - GMP_NUMB_BITS;
86 /* searching for the first bit 1 (exists since u isn't an integer) */
87 while (up[--un] == 0)
88 re -= GMP_NUMB_BITS;
89 MPFR_ASSERTN(un >= 0);
90 k = up[un];
91 count_leading_zeros(sh, k);
92 re -= sh;
93 k <<= sh;
94 }
95 /* The exponent of r will be re */
96 /* un: index of the limb of u that contains the first bit 1 of the FP */
97
98 t = (mp_size_t) (MPFR_PREC(r) - 1) / GMP_NUMB_BITS < un ?
99 (mpfr_init2 (tmp, (un + 1) * GMP_NUMB_BITS), tmp) : r;
100 /* t has enough precision to contain the fractional part of u */
101 /* If we use a temporary variable, we take the non-significant bits
102 of u into account, because of the mpn_lshift below. */
103 MPFR_SET_SAME_SIGN(t, u);
104
105 /* Put the fractional part of u into t */
106 tn = (MPFR_PREC(t) - 1) / GMP_NUMB_BITS;
107 MPFR_ASSERTN(tn >= un);
108 t0 = tn - un;
109 tp = MPFR_MANT(t);
110 if (sh == 0)
111 mpn_copyd (tp + t0, up, un + 1);
112 else /* warning: un may be 0 here */
113 tp[tn] = k | ((un) ? mpn_lshift (tp + t0, up, un, sh) : MPFR_LIMB_ZERO);
114 if (t0 > 0)
115 MPN_ZERO(tp, t0);
116
117 MPFR_SAVE_EXPO_MARK (expo);
118
119 if (t != r)
120 { /* t is tmp */
121 MPFR_EXP (t) = 0; /* should be re, but not necessarily in the range */
122 inex = mpfr_set (r, t, rnd_mode); /* no underflow */
123 mpfr_clear (t);
124 MPFR_EXP (r) += re;
125 }
126 else
127 { /* There may be remaining non-significant bits in t (= r). */
128 int carry;
129
130 MPFR_EXP (r) = re;
131 carry = mpfr_round_raw (tp, tp,
132 (mpfr_prec_t) (tn + 1) * GMP_NUMB_BITS,
133 MPFR_IS_NEG (r), MPFR_PREC (r), rnd_mode,
134 &inex);
135 if (carry)
136 {
137 tp[tn] = MPFR_LIMB_HIGHBIT;
138 MPFR_EXP (r) ++;
139 }
140 }
141
142 MPFR_SAVE_EXPO_FREE (expo);
143 return mpfr_check_range (r, inex, rnd_mode);
144 }