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      1 /* mpfr_eq -- Compare two floats up to a specified bit #.
      2 
      3 Copyright 1999, 2001, 2003-2004, 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 #include "mpfr-impl.h"
     25 
     26 /* return non-zero if the first n_bits bits of u, v are equal,
     27    0 otherwise */
     28 int
     29 mpfr_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