1/* mpfr_eq -- Compare two floats up to a specified bit #.
2
3Copyright 1999, 2001, 2003, 2004, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013 Free Software Foundation, Inc.
4Contributed by the AriC and Caramel 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
20http://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc.,
2151 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */
22
23
24#include "mpfr-impl.h"
25
26/* return non-zero if the first n_bits bits of u, v are equal,
27   0 otherwise */
28int
29mpfr_eq (mpfr_srcptr u, mpfr_srcptr v, unsigned long int n_bits)
30{
31  mpfr_limb_srcptr up, vp;
32  mp_size_t usize, vsize, size, i;
33  mpfr_exp_t uexp, vexp;
34  int k;
35
36  if (MPFR_ARE_SINGULAR(u, v))
37    {
38      if (MPFR_IS_NAN(u) || MPFR_IS_NAN(v))
39        return 0; /* non equal */
40      else if (MPFR_IS_INF(u) && MPFR_IS_INF(v))
41        return (MPFR_SIGN(u) == MPFR_SIGN(v));
42      else if (MPFR_IS_ZERO(u) && MPFR_IS_ZERO(v))
43        return 1;
44      else
45        return 0;
46    }
47
48  /* 1. Are the signs different?  */
49  if (MPFR_SIGN(u) != MPFR_SIGN(v))
50    return 0;
51
52  uexp = MPFR_GET_EXP (u);
53  vexp = MPFR_GET_EXP (v);
54
55  /* 2. Are the exponents different?  */
56  if (uexp != vexp)
57    return 0; /* no bit agree */
58
59  usize = MPFR_LIMB_SIZE (u);
60  vsize = MPFR_LIMB_SIZE (v);
61
62  if (vsize > usize) /* exchange u and v */
63    {
64      up = MPFR_MANT(v);
65      vp = MPFR_MANT(u);
66      size = vsize;
67      vsize = usize;
68      usize = size;
69    }
70  else
71    {
72      up = MPFR_MANT(u);
73      vp = MPFR_MANT(v);
74    }
75
76  /* now usize >= vsize */
77  MPFR_ASSERTD(usize >= vsize);
78
79  if (usize > vsize)
80    {
81      if ((unsigned long) vsize * GMP_NUMB_BITS < n_bits)
82        {
83          /* check if low min(PREC(u), n_bits) - (vsize * GMP_NUMB_BITS)
84             bits from u are non-zero */
85          unsigned long remains = n_bits - (vsize * GMP_NUMB_BITS);
86          k = usize - vsize - 1;
87          while (k >= 0 && remains >= GMP_NUMB_BITS && !up[k])
88            {
89              k--;
90              remains -= GMP_NUMB_BITS;
91            }
92          /* now either k < 0: all low bits from u are zero
93                 or remains < GMP_NUMB_BITS: check high bits from up[k]
94                 or up[k] <> 0: different */
95          if (k >= 0 && (((remains < GMP_NUMB_BITS) &&
96                          (up[k] >> (GMP_NUMB_BITS - remains))) ||
97                         (remains >= GMP_NUMB_BITS && up[k])))
98            return 0;           /* surely too different */
99        }
100      size = vsize;
101    }
102  else
103    {
104      size = usize;
105    }
106
107  /* now size = min (usize, vsize) */
108
109  /* If size is too large wrt n_bits, reduce it to look only at the
110     high n_bits bits.
111     Otherwise, if n_bits > size * GMP_NUMB_BITS, reduce n_bits to
112     size * GMP_NUMB_BITS, since the extra low bits of one of the
113     operands have already been check above. */
114  if ((unsigned long) size > 1 + (n_bits - 1) / GMP_NUMB_BITS)
115    size = 1 + (n_bits - 1) / GMP_NUMB_BITS;
116  else if (n_bits > (unsigned long) size * GMP_NUMB_BITS)
117    n_bits = size * GMP_NUMB_BITS;
118
119  up += usize - size;
120  vp += vsize - size;
121
122  for (i = size - 1; i > 0 && n_bits >= GMP_NUMB_BITS; i--)
123    {
124      if (up[i] != vp[i])
125        return 0;
126      n_bits -= GMP_NUMB_BITS;
127    }
128
129  /* now either i=0 or n_bits<GMP_NUMB_BITS */
130
131  /* since n_bits <= size * GMP_NUMB_BITS before the above for-loop,
132     we have the invariant n_bits <= (i+1) * GMP_NUMB_BITS, thus
133     we always have n_bits <= GMP_NUMB_BITS here */
134  MPFR_ASSERTD(n_bits <= GMP_NUMB_BITS);
135
136  if (n_bits & (GMP_NUMB_BITS - 1))
137    return (up[i] >> (GMP_NUMB_BITS - (n_bits & (GMP_NUMB_BITS - 1))) ==
138            vp[i] >> (GMP_NUMB_BITS - (n_bits & (GMP_NUMB_BITS - 1))));
139  else
140    return (up[i] == vp[i]);
141}
142