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/* mpf_div_2exp -- Divide a float by 2^n.
Copyright 1993, 1994, 1996, 2000-2002, 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 https://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;
}
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