div_2exp.c

/* mpf_div_2exp -- Divide a float by 2^n.

Copyright 1993, 1994, 1996, 2000, 2001, 2002, 2004 Free Software Foundation,
Inc.

This file is part of the GNU MP Library.

The GNU MP Library is free software; you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation; either version 3 of the License, or (at your
option) any later version.

The GNU MP Library is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
License for more details.

You should have received a copy of the GNU Lesser General Public License
along with the GNU MP Library.  If not, see http://www.gnu.org/licenses/.  */

#include "gmp.h"
#include "gmp-impl.h"


/* Multiples of GMP_NUMB_BITS in exp simply mean an amount subtracted from
   EXP(u) to set EXP(r).  The remainder exp%GMP_NUMB_BITS is then a right
   shift for the limb data.

   If exp%GMP_NUMB_BITS == 0 then there's no shifting, we effectively just
   do an mpz_set with changed EXP(r).  Like mpz_set we take prec+1 limbs in
   this case.  Although just prec would suffice, it's nice to have
   mpf_div_2exp with exp==0 come out the same as mpz_set.

   When shifting we take up to prec many limbs from the input.  Our shift is
   cy = mpn_rshift (PTR(r)+1, PTR(u)+k, ...), where k is the number of low
   limbs dropped from u, and the carry out is stored to PTR(r)[0].  We don't
   try to work extra bits from PTR(u)[k-1] (when k>=1 makes it available)
   into that low carry limb.  Just prec limbs (with the high non-zero) from
   the input is enough bits for the application requested precision, no need
   to do extra work.

   If r==u the shift will have overlapping operands.  When k>=1 (ie. when
   usize > prec), the overlap is in the style supported by rshift (ie. dst
   <= src).

   But when r==u and k==0 (ie. usize <= prec), we would have an invalid
   overlap (mpn_rshift (rp+1, rp, ...)).  In this case we must instead use
   mpn_lshift (PTR(r), PTR(u), size, NUMB-shift).  An lshift by NUMB-shift
   bits gives identical data of course, it's just its overlap restrictions
   which differ.

   In both shift cases, the resulting data is abs_usize+1 limbs.  "adj" is
   used to add +1 to that size if the high is non-zero (it may of course
   have become zero by the shifting).  EXP(u) is the exponent just above
   those abs_usize+1 limbs, so it gets -1+adj, which means -1 if the high is
   zero, or no change if the high is non-zero.

   Enhancements:

   The way mpn_lshift is used means successive mpf_div_2exp calls on the
   same operand will accumulate low zero limbs, until prec+1 limbs is
   reached.  This is wasteful for subsequent operations.  When abs_usize <=
   prec, we should test the low exp%GMP_NUMB_BITS many bits of PTR(u)[0],
   ie. those which would be shifted out by an mpn_rshift.  If they're zero
   then use that mpn_rshift.  */

void
mpf_div_2exp (mpf_ptr r, mpf_srcptr u, mp_bitcnt_t exp)
{
  mp_srcptr up;
  mp_ptr rp = r->_mp_d;
  mp_size_t usize;
  mp_size_t abs_usize;
  mp_size_t prec = r->_mp_prec;
  mp_exp_t uexp = u->_mp_exp;

  usize = u->_mp_size;

  if (UNLIKELY (usize == 0))
    {
      r->_mp_size = 0;
      r->_mp_exp = 0;
      return;
    }

  abs_usize = ABS (usize);
  up = u->_mp_d;

  if (exp % GMP_NUMB_BITS == 0)
    {
      prec++;			/* retain more precision here as we don't need
				   to account for carry-out here */
      if (abs_usize > prec)
	{
	  up += abs_usize - prec;
	  abs_usize = prec;
	}
      if (rp != up)
	MPN_COPY_INCR (rp, up, abs_usize);
      r->_mp_exp = uexp - exp / GMP_NUMB_BITS;
    }
  else
    {
      mp_limb_t cy_limb;
      mp_size_t adj;
      if (abs_usize > prec)
	{
	  up += abs_usize - prec;
	  abs_usize = prec;
	  /* Use mpn_rshift since mpn_lshift operates downwards, and we
	     therefore would clobber part of U before using that part, in case
	     R is the same variable as U.  */
	  cy_limb = mpn_rshift (rp + 1, up, abs_usize, exp % GMP_NUMB_BITS);
	  rp[0] = cy_limb;
	  adj = rp[abs_usize] != 0;
	}
      else
	{
	  cy_limb = mpn_lshift (rp, up, abs_usize,
				GMP_NUMB_BITS - exp % GMP_NUMB_BITS);
	  rp[abs_usize] = cy_limb;
	  adj = cy_limb != 0;
	}

      abs_usize += adj;
      r->_mp_exp = uexp - exp / GMP_NUMB_BITS - 1 + adj;
    }
  r->_mp_size = usize >= 0 ? abs_usize : -abs_usize;
}