github.com/aergoio/aergo@v1.3.1/libtool/src/gmp-6.1.2/mpf/div_2exp.c (about)

     1  /* mpf_div_2exp -- Divide a float by 2^n.
     2  
     3  Copyright 1993, 1994, 1996, 2000-2002, 2004 Free Software Foundation, Inc.
     4  
     5  This file is part of the GNU MP Library.
     6  
     7  The GNU MP Library is free software; you can redistribute it and/or modify
     8  it under the terms of either:
     9  
    10    * the GNU Lesser General Public License as published by the Free
    11      Software Foundation; either version 3 of the License, or (at your
    12      option) any later version.
    13  
    14  or
    15  
    16    * the GNU General Public License as published by the Free Software
    17      Foundation; either version 2 of the License, or (at your option) any
    18      later version.
    19  
    20  or both in parallel, as here.
    21  
    22  The GNU MP Library is distributed in the hope that it will be useful, but
    23  WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
    24  or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
    25  for more details.
    26  
    27  You should have received copies of the GNU General Public License and the
    28  GNU Lesser General Public License along with the GNU MP Library.  If not,
    29  see https://www.gnu.org/licenses/.  */
    30  
    31  #include "gmp.h"
    32  #include "gmp-impl.h"
    33  
    34  
    35  /* Multiples of GMP_NUMB_BITS in exp simply mean an amount subtracted from
    36     EXP(u) to set EXP(r).  The remainder exp%GMP_NUMB_BITS is then a right
    37     shift for the limb data.
    38  
    39     If exp%GMP_NUMB_BITS == 0 then there's no shifting, we effectively just
    40     do an mpz_set with changed EXP(r).  Like mpz_set we take prec+1 limbs in
    41     this case.  Although just prec would suffice, it's nice to have
    42     mpf_div_2exp with exp==0 come out the same as mpz_set.
    43  
    44     When shifting we take up to prec many limbs from the input.  Our shift is
    45     cy = mpn_rshift (PTR(r)+1, PTR(u)+k, ...), where k is the number of low
    46     limbs dropped from u, and the carry out is stored to PTR(r)[0].  We don't
    47     try to work extra bits from PTR(u)[k-1] (when k>=1 makes it available)
    48     into that low carry limb.  Just prec limbs (with the high non-zero) from
    49     the input is enough bits for the application requested precision, no need
    50     to do extra work.
    51  
    52     If r==u the shift will have overlapping operands.  When k>=1 (ie. when
    53     usize > prec), the overlap is in the style supported by rshift (ie. dst
    54     <= src).
    55  
    56     But when r==u and k==0 (ie. usize <= prec), we would have an invalid
    57     overlap (mpn_rshift (rp+1, rp, ...)).  In this case we must instead use
    58     mpn_lshift (PTR(r), PTR(u), size, NUMB-shift).  An lshift by NUMB-shift
    59     bits gives identical data of course, it's just its overlap restrictions
    60     which differ.
    61  
    62     In both shift cases, the resulting data is abs_usize+1 limbs.  "adj" is
    63     used to add +1 to that size if the high is non-zero (it may of course
    64     have become zero by the shifting).  EXP(u) is the exponent just above
    65     those abs_usize+1 limbs, so it gets -1+adj, which means -1 if the high is
    66     zero, or no change if the high is non-zero.
    67  
    68     Enhancements:
    69  
    70     The way mpn_lshift is used means successive mpf_div_2exp calls on the
    71     same operand will accumulate low zero limbs, until prec+1 limbs is
    72     reached.  This is wasteful for subsequent operations.  When abs_usize <=
    73     prec, we should test the low exp%GMP_NUMB_BITS many bits of PTR(u)[0],
    74     ie. those which would be shifted out by an mpn_rshift.  If they're zero
    75     then use that mpn_rshift.  */
    76  
    77  void
    78  mpf_div_2exp (mpf_ptr r, mpf_srcptr u, mp_bitcnt_t exp)
    79  {
    80    mp_srcptr up;
    81    mp_ptr rp = r->_mp_d;
    82    mp_size_t usize;
    83    mp_size_t abs_usize;
    84    mp_size_t prec = r->_mp_prec;
    85    mp_exp_t uexp = u->_mp_exp;
    86  
    87    usize = u->_mp_size;
    88  
    89    if (UNLIKELY (usize == 0))
    90      {
    91        r->_mp_size = 0;
    92        r->_mp_exp = 0;
    93        return;
    94      }
    95  
    96    abs_usize = ABS (usize);
    97    up = u->_mp_d;
    98  
    99    if (exp % GMP_NUMB_BITS == 0)
   100      {
   101        prec++;			/* retain more precision here as we don't need
   102  				   to account for carry-out here */
   103        if (abs_usize > prec)
   104  	{
   105  	  up += abs_usize - prec;
   106  	  abs_usize = prec;
   107  	}
   108        if (rp != up)
   109  	MPN_COPY_INCR (rp, up, abs_usize);
   110        r->_mp_exp = uexp - exp / GMP_NUMB_BITS;
   111      }
   112    else
   113      {
   114        mp_limb_t cy_limb;
   115        mp_size_t adj;
   116        if (abs_usize > prec)
   117  	{
   118  	  up += abs_usize - prec;
   119  	  abs_usize = prec;
   120  	  /* Use mpn_rshift since mpn_lshift operates downwards, and we
   121  	     therefore would clobber part of U before using that part, in case
   122  	     R is the same variable as U.  */
   123  	  cy_limb = mpn_rshift (rp + 1, up, abs_usize, exp % GMP_NUMB_BITS);
   124  	  rp[0] = cy_limb;
   125  	  adj = rp[abs_usize] != 0;
   126  	}
   127        else
   128  	{
   129  	  cy_limb = mpn_lshift (rp, up, abs_usize,
   130  				GMP_NUMB_BITS - exp % GMP_NUMB_BITS);
   131  	  rp[abs_usize] = cy_limb;
   132  	  adj = cy_limb != 0;
   133  	}
   134  
   135        abs_usize += adj;
   136        r->_mp_exp = uexp - exp / GMP_NUMB_BITS - 1 + adj;
   137      }
   138    r->_mp_size = usize >= 0 ? abs_usize : -abs_usize;
   139  }