source/libs/gmp/gmp-src/mpf/div_2exp.c

   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 }