1 /* mpfr_set_q -- set a floating-point number from a multiple-precision rational
2
3 Copyright 2000-2002, 2004-2023 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 #define MPFR_NEED_LONGLONG_H
24 #include "mpfr-impl.h"
25
26 #ifndef MPFR_USE_MINI_GMP
27 /*
28 * Set f to z, choosing the smallest precision for f
29 * so that z = f*(2^BPML)*zs*2^(RetVal)
30 */
31 static int
set_z(mpfr_ptr f,mpz_srcptr z,mp_size_t * zs)32 set_z (mpfr_ptr f, mpz_srcptr z, mp_size_t *zs)
33 {
34 mp_limb_t *p;
35 mp_size_t s;
36 int c;
37 mpfr_prec_t pf;
38
39 MPFR_ASSERTD (mpz_sgn (z) != 0);
40
41 /* Remove useless ending 0 */
42 for (p = PTR (z), s = *zs = ABSIZ (z) ; *p == 0; p++, s--)
43 MPFR_ASSERTD (s >= 0);
44
45 /* Get working precision */
46 count_leading_zeros (c, p[s-1]);
47 pf = s * GMP_NUMB_BITS - c;
48 MPFR_ASSERTD (pf >= 1);
49 mpfr_init2 (f, pf >= MPFR_PREC_MIN ? pf : MPFR_PREC_MIN);
50
51 /* Copy Mantissa */
52 if (MPFR_LIKELY (c))
53 mpn_lshift (MPFR_MANT (f), p, s, c);
54 else
55 MPN_COPY (MPFR_MANT (f), p, s);
56
57 MPFR_SET_SIGN (f, mpz_sgn (z));
58 MPFR_SET_EXP (f, 0);
59
60 return -c;
61 }
62
63 /* set f to the rational q */
64 int
mpfr_set_q(mpfr_ptr f,mpq_srcptr q,mpfr_rnd_t rnd)65 mpfr_set_q (mpfr_ptr f, mpq_srcptr q, mpfr_rnd_t rnd)
66 {
67 mpz_srcptr num, den;
68 mpfr_t n, d;
69 int inexact;
70 int cn, cd;
71 long shift;
72 mp_size_t sn, sd;
73 MPFR_SAVE_EXPO_DECL (expo);
74
75 num = mpq_numref (q);
76 den = mpq_denref (q);
77 /* NAN and INF for mpq are not really documented, but could be found */
78 if (MPFR_UNLIKELY (mpz_sgn (num) == 0))
79 {
80 if (MPFR_UNLIKELY (mpz_sgn (den) == 0))
81 {
82 MPFR_SET_NAN (f);
83 MPFR_RET_NAN;
84 }
85 else
86 {
87 MPFR_SET_ZERO (f);
88 MPFR_SET_POS (f);
89 MPFR_RET (0);
90 }
91 }
92 if (MPFR_UNLIKELY (mpz_sgn (den) == 0))
93 {
94 MPFR_SET_INF (f);
95 MPFR_SET_SIGN (f, mpz_sgn (num));
96 MPFR_RET (0);
97 }
98
99 MPFR_SAVE_EXPO_MARK (expo);
100
101 cn = set_z (n, num, &sn);
102 cd = set_z (d, den, &sd);
103
104 /* sn is the number of limbs of the numerator, sd that of the denominator */
105
106 sn -= sd;
107 #if GMP_NUMB_BITS <= 32 /* overflow/underflow cannot happen on 64-bit
108 processors, where MPFR_EMAX_MAX is 2^62 - 1, due to
109 memory limits */
110 /* If sn >= 0, the quotient has at most sn limbs, thus is larger or equal to
111 2^((sn-1)*GMP_NUMB_BITS), thus its exponent >= (sn-1)*GMP_NUMB_BITS)+1.
112 (sn-1)*GMP_NUMB_BITS)+1 > emax yields (sn-1)*GMP_NUMB_BITS) >= emax,
113 i.e., sn-1 >= floor(emax/GMP_NUMB_BITS). */
114 if (MPFR_UNLIKELY (sn > MPFR_EMAX_MAX / GMP_NUMB_BITS))
115 {
116 MPFR_SAVE_EXPO_FREE (expo);
117 inexact = mpfr_overflow (f, rnd, MPFR_SIGN (f));
118 goto end;
119 }
120 /* If sn < 0, the inverse quotient is >= 2^((-sn-1)*GMP_NUMB_BITS),
121 thus the quotient is <= 2^((sn+1)*GMP_NUMB_BITS), and thus its
122 exponent is <= (sn+1)*GMP_NUMB_BITS+1.
123 (sn+1)*GMP_NUMB_BITS+1 < emin yields (sn+1)*GMP_NUMB_BITS+2 <= emin,
124 i.e., sn+1 <= floor((emin-2)/GMP_NUMB_BITS). */
125 if (MPFR_UNLIKELY (sn <= (MPFR_EMIN_MIN - 2) / GMP_NUMB_BITS - 1))
126 {
127 MPFR_SAVE_EXPO_FREE (expo);
128 if (rnd == MPFR_RNDN)
129 rnd = MPFR_RNDZ;
130 inexact = mpfr_underflow (f, rnd, MPFR_SIGN (f));
131 goto end;
132 }
133 #endif
134
135 inexact = mpfr_div (f, n, d, rnd);
136 shift = GMP_NUMB_BITS*sn+cn-cd;
137 MPFR_ASSERTD (shift == GMP_NUMB_BITS*sn+cn-cd);
138 cd = mpfr_mul_2si (f, f, shift, rnd);
139 MPFR_SAVE_EXPO_FREE (expo);
140 /* we can have cd <> 0 only in case of underflow or overflow, but since we
141 are still in extended exponent range, this cannot happen on 64-bit (see
142 above) */
143 #if GMP_NUMB_BITS <= 32
144 if (MPFR_UNLIKELY (cd != 0))
145 inexact = cd;
146 else
147 inexact = mpfr_check_range (f, inexact, rnd);
148 end:
149 #else
150 MPFR_ASSERTD(cd == 0);
151 inexact = mpfr_check_range (f, inexact, rnd);
152 #endif
153 mpfr_clear (d);
154 mpfr_clear (n);
155 MPFR_RET (inexact);
156 }
157 #endif
158