1/* mpfr_set_q -- set a floating-point number from a multiple-precision rational
2
3Copyright 2000-2002, 2004-2023 Free Software Foundation, Inc.
4Contributed by the AriC and Caramba projects, INRIA.
5
6This file is part of the GNU MPFR Library.
7
8The GNU MPFR Library is free software; you can redistribute it and/or modify
9it under the terms of the GNU Lesser General Public License as published by
10the Free Software Foundation; either version 3 of the License, or (at your
11option) any later version.
12
13The GNU MPFR Library is distributed in the hope that it will be useful, but
14WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
15or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
16License for more details.
17
18You should have received a copy of the GNU Lesser General Public License
19along with the GNU MPFR Library; see the file COPYING.LESSER.  If not, see
20https://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc.,
2151 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 */
31static int
32set_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 */
64int
65mpfr_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