contrib/gmp/mpf/div_2exp.c

   1 /* mpf_div_2exp -- Divide a float by 2^n.
   2
   3 Copyright 1993, 1994, 1996, 2000, 2001, 2002, 2004 Free Software Foundation,
   4 Inc.
   5
   6 This file is part of the GNU MP Library.
   7
   8 The GNU MP 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 MP 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 MP Library.  If not, see http://www.gnu.org/licenses/.  */
  20
  21 #include "gmp.h"
  22 #include "gmp-impl.h"
  23
  24
  25 /* Multiples of GMP_NUMB_BITS in exp simply mean an amount subtracted from
  26    EXP(u) to set EXP(r).  The remainder exp%GMP_NUMB_BITS is then a right
  27    shift for the limb data.
  28
  29    If exp%GMP_NUMB_BITS == 0 then there's no shifting, we effectively just
  30    do an mpz_set with changed EXP(r).  Like mpz_set we take prec+1 limbs in
  31    this case.  Although just prec would suffice, it's nice to have
  32    mpf_div_2exp with exp==0 come out the same as mpz_set.
  33
  34    When shifting we take up to prec many limbs from the input.  Our shift is
  35    cy = mpn_rshift (PTR(r)+1, PTR(u)+k, ...), where k is the number of low
  36    limbs dropped from u, and the carry out is stored to PTR(r)[0].  We don't
  37    try to work extra bits from PTR(u)[k-1] (when k>=1 makes it available)
  38    into that low carry limb.  Just prec limbs (with the high non-zero) from
  39    the input is enough bits for the application requested precision, no need
  40    to do extra work.
  41
  42    If r==u the shift will have overlapping operands.  When k>=1 (ie. when
  43    usize > prec), the overlap is in the style supported by rshift (ie. dst
  44    <= src).
  45
  46    But when r==u and k==0 (ie. usize <= prec), we would have an invalid
  47    overlap (mpn_rshift (rp+1, rp, ...)).  In this case we must instead use
  48    mpn_lshift (PTR(r), PTR(u), size, NUMB-shift).  An lshift by NUMB-shift
  49    bits gives identical data of course, it's just its overlap restrictions
  50    which differ.
  51
  52    In both shift cases, the resulting data is abs_usize+1 limbs.  "adj" is
  53    used to add +1 to that size if the high is non-zero (it may of course
  54    have become zero by the shifting).  EXP(u) is the exponent just above
  55    those abs_usize+1 limbs, so it gets -1+adj, which means -1 if the high is
  56    zero, or no change if the high is non-zero.
  57
  58    Enhancements:
  59
  60    The way mpn_lshift is used means successive mpf_div_2exp calls on the
  61    same operand will accumulate low zero limbs, until prec+1 limbs is
  62    reached.  This is wasteful for subsequent operations.  When abs_usize <=
  63    prec, we should test the low exp%GMP_NUMB_BITS many bits of PTR(u)[0],
  64    ie. those which would be shifted out by an mpn_rshift.  If they're zero
  65    then use that mpn_rshift.  */
  66
  67 void
  68 mpf_div_2exp (mpf_ptr r, mpf_srcptr u, mp_bitcnt_t exp)
  69 {
  70   mp_srcptr up;
  71   mp_ptr rp = r->_mp_d;
  72   mp_size_t usize;
  73   mp_size_t abs_usize;
  74   mp_size_t prec = r->_mp_prec;
  75   mp_exp_t uexp = u->_mp_exp;
  76
  77   usize = u->_mp_size;
  78
  79   if (UNLIKELY (usize == 0))
  80     {
  81       r->_mp_size = 0;
  82       r->_mp_exp = 0;
  83       return;
  84     }
  85
  86   abs_usize = ABS (usize);
  87   up = u->_mp_d;
  88
  89   if (exp % GMP_NUMB_BITS == 0)
  90     {
  91       prec++;                   /* retain more precision here as we don't need
  92                                    to account for carry-out here */
  93       if (abs_usize > prec)
  94         {
  95           up += abs_usize - prec;
  96           abs_usize = prec;
  97         }
  98       if (rp != up)
  99         MPN_COPY_INCR (rp, up, abs_usize);
 100       r->_mp_exp = uexp - exp / GMP_NUMB_BITS;
 101     }
 102   else
 103     {
 104       mp_limb_t cy_limb;
 105       mp_size_t adj;
 106       if (abs_usize > prec)
 107         {
 108           up += abs_usize - prec;
 109           abs_usize = prec;
 110           /* Use mpn_rshift since mpn_lshift operates downwards, and we
 111              therefore would clobber part of U before using that part, in case
 112              R is the same variable as U.  */
 113           cy_limb = mpn_rshift (rp + 1, up, abs_usize, exp % GMP_NUMB_BITS);
 114           rp[0] = cy_limb;
 115           adj = rp[abs_usize] != 0;
 116         }
 117       else
 118         {
 119           cy_limb = mpn_lshift (rp, up, abs_usize,
 120                                 GMP_NUMB_BITS - exp % GMP_NUMB_BITS);
 121           rp[abs_usize] = cy_limb;
 122           adj = cy_limb != 0;
 123         }
 124
 125       abs_usize += adj;
 126       r->_mp_exp = uexp - exp / GMP_NUMB_BITS - 1 + adj;
 127     }
 128   r->_mp_size = usize >= 0 ? abs_usize : -abs_usize;
 129 }