/* 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 either:
* 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.
or
* the GNU General Public License as published by the Free Software
Foundation; either version 2 of the License, or (at your option) any
later version.
or both in parallel, as here.
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 General Public License
for more details.
You should have received copies of the GNU General Public License and the
GNU Lesser General Public License along with the GNU MP Library. If not,
see https://www.gnu.org/licenses/. */
#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;
}