/* mpfr_round_raw_generic -- Generic rounding function
Copyright 1999-2023 Free Software Foundation, Inc.
Contributed by the AriC and Caramba projects, INRIA.
This file is part of the GNU MPFR Library.
The GNU MPFR 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 MPFR 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 MPFR Library; see the file COPYING.LESSER. If not, see
https://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc.,
51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */
#ifndef flag
# error "ERROR: flag must be defined (0 / 1)"
#endif
#ifndef use_inexp
# error "ERROR: use_enexp must be defined (0 / 1)"
#endif
#ifndef mpfr_round_raw_generic
# error "ERROR: mpfr_round_raw_generic must be defined"
#endif
/*
* If flag = 0, puts in y the value of xp (with precision xprec and
* sign 1 if negative=0, -1 otherwise) rounded to precision yprec and
* direction rnd_mode. Supposes x is not zero nor NaN nor +/- Infinity
* (i.e. *xp != 0). In that case, the return value is a possible carry
* (0 or 1) that may happen during the rounding, in which case the result
* is a power of two.
*
* If inexp != NULL, put in *inexp the inexact flag of the rounding (0, 1, -1).
* In case of even rounding when rnd = MPFR_RNDN, put MPFR_EVEN_INEX (2) or
* -MPFR_EVEN_INEX (-2) in *inexp.
*
* If flag = 1, just returns whether one should add 1 or not for rounding.
*
* Note: yprec may be < MPFR_PREC_MIN; in particular, it may be equal
* to 1. In this case, the even rounding is done away from 0, which is
* a natural generalization. Indeed, a number with 1-bit precision can
* be seen as a subnormal number with more precision.
*
* MPFR_RNDNA is now supported, but needs to be tested [TODO] and is
* still not part of the API. In particular, the MPFR_RNDNA value (-1)
* may change in the future without notice.
*/
#if !(flag == 0 || flag == 1)
#error "flag must be 0 or 1"
#endif
int
mpfr_round_raw_generic(
#if flag == 0
mp_limb_t *yp,
#endif
const mp_limb_t *xp, mpfr_prec_t xprec,
int neg, mpfr_prec_t yprec, mpfr_rnd_t rnd_mode
#if use_inexp != 0
, int *inexp
#endif
)
{
mp_size_t xsize, nw;
mp_limb_t himask, lomask, sb;
int rw, new_use_inexp;
#if flag == 0
int carry;
#endif
#if use_inexp != 0
MPFR_ASSERTD (inexp != ((int*) 0));
#endif
MPFR_ASSERTD (neg == 0 || neg == 1);
#if flag == 1
/* rnd_mode = RNDF is only possible for flag = 0. */
MPFR_ASSERTD (rnd_mode != MPFR_RNDF);
#endif
if (rnd_mode == MPFR_RNDF)
{
#if use_inexp != 0
*inexp = 0; /* make sure it has a valid value */
#endif
rnd_mode = MPFR_RNDZ; /* faster */
new_use_inexp = 0;
}
else
{
if (flag && !use_inexp &&
(xprec <= yprec || MPFR_IS_LIKE_RNDZ (rnd_mode, neg)))
return 0;
new_use_inexp = use_inexp;
}
xsize = MPFR_PREC2LIMBS (xprec);
nw = yprec / GMP_NUMB_BITS;
rw = yprec & (GMP_NUMB_BITS - 1);
if (MPFR_UNLIKELY(xprec <= yprec))
{ /* No rounding is necessary. */
/* if yp=xp, maybe an overlap: mpn_copyd is OK when src <= dst */
if (MPFR_LIKELY(rw))
nw++;
MPFR_ASSERTD(nw >= 1);
MPFR_ASSERTD(nw >= xsize);
#if use_inexp != 0
*inexp = 0;
#endif
#if flag == 0
mpn_copyd (yp + (nw - xsize), xp, xsize);
MPN_ZERO(yp, nw - xsize);
#endif
return 0;
}
if (new_use_inexp || !MPFR_IS_LIKE_RNDZ(rnd_mode, neg))
{
mp_size_t k = xsize - nw - 1;
if (MPFR_LIKELY(rw))
{
nw++;
lomask = MPFR_LIMB_MASK (GMP_NUMB_BITS - rw);
himask = ~lomask;
}
else
{
lomask = MPFR_LIMB_MAX;
himask = MPFR_LIMB_MAX;
}
MPFR_ASSERTD(k >= 0);
sb = xp[k] & lomask; /* First non-significant bits */
/* Rounding to nearest? */
if (rnd_mode == MPFR_RNDN || rnd_mode == MPFR_RNDNA)
{
/* Rounding to nearest */
mp_limb_t rbmask = MPFR_LIMB_ONE << (GMP_NUMB_BITS - 1 - rw);
if ((sb & rbmask) == 0) /* rounding bit = 0 ? */
goto rnd_RNDZ; /* yes, behave like rounding toward zero */
/* Rounding to nearest with rounding bit = 1 */
if (MPFR_UNLIKELY (rnd_mode == MPFR_RNDNA))
goto away_addone_ulp; /* like rounding away from zero */
sb &= ~rbmask; /* first bits after the rounding bit */
while (MPFR_UNLIKELY(sb == 0) && k > 0)
sb = xp[--k];
if (MPFR_UNLIKELY(sb == 0)) /* Even rounding. */
{
/* sb == 0 && rnd_mode == MPFR_RNDN */
sb = xp[xsize - nw] & (himask ^ (himask << 1));
if (sb == 0)
{
#if use_inexp != 0
*inexp = 2 * MPFR_EVEN_INEX * neg - MPFR_EVEN_INEX;
#endif
/* ((neg!=0)^(sb!=0)) ? MPFR_EVEN_INEX : -MPFR_EVEN_INEX */
/* since neg = 0 or 1 and sb = 0 */
#if flag == 0
mpn_copyi (yp, xp + xsize - nw, nw);
yp[0] &= himask;
#endif
return 0; /* sb != 0 && rnd_mode != MPFR_RNDZ */
}
else
{
away_addone_ulp:
/* sb != 0 && rnd_mode == MPFR_RNDN */
#if use_inexp != 0
*inexp = MPFR_EVEN_INEX - 2 * MPFR_EVEN_INEX * neg;
#endif
/* ((neg!=0)^(sb!=0)) ? MPFR_EVEN_INEX : -MPFR_EVEN_INEX */
/* since neg = 0 or 1 and sb != 0 */
goto rnd_RNDN_add_one_ulp;
}
}
else /* sb != 0 && rnd_mode == MPFR_RNDN */
{
#if use_inexp != 0
*inexp = 1 - 2 * neg; /* neg == 0 ? 1 : -1 */
#endif
rnd_RNDN_add_one_ulp:
#if flag == 1
return 1; /* sb != 0 && rnd_mode != MPFR_RNDZ */
#else
carry = mpn_add_1 (yp, xp + xsize - nw, nw,
rw ?
MPFR_LIMB_ONE << (GMP_NUMB_BITS - rw)
: MPFR_LIMB_ONE);
yp[0] &= himask;
return carry;
#endif
}
}
/* Rounding toward zero? */
else if (MPFR_IS_LIKE_RNDZ(rnd_mode, neg))
{
/* rnd_mode == MPFR_RNDZ */
rnd_RNDZ:
while (MPFR_UNLIKELY (sb == 0) && k > 0)
sb = xp[--k];
#if use_inexp != 0
/* rnd_mode == MPFR_RNDZ and neg = 0 or 1 */
/* ((neg != 0) ^ (rnd_mode != MPFR_RNDZ)) ? 1 : -1 */
*inexp = MPFR_UNLIKELY (sb == 0) ? 0 : 2 * neg - 1;
#endif
#if flag == 0
mpn_copyi (yp, xp + xsize - nw, nw);
yp[0] &= himask;
#endif
return 0; /* sb != 0 && rnd_mode != MPFR_RNDZ */
}
else
{
/* Rounding away from zero */
while (MPFR_UNLIKELY (sb == 0) && k > 0)
sb = xp[--k];
if (MPFR_UNLIKELY (sb == 0))
{
/* sb = 0 && rnd_mode != MPFR_RNDZ */
#if use_inexp != 0
/* ((neg != 0) ^ (rnd_mode != MPFR_RNDZ)) ? 1 : -1 */
*inexp = 0;
#endif
#if flag == 0
mpn_copyi (yp, xp + xsize - nw, nw);
yp[0] &= himask;
#endif
return 0;
}
else
{
/* sb != 0 && rnd_mode != MPFR_RNDZ */
#if use_inexp != 0
*inexp = 1 - 2 * neg; /* neg == 0 ? 1 : -1 */
#endif
#if flag == 1
return 1;
#else
carry = mpn_add_1(yp, xp + xsize - nw, nw,
rw ? MPFR_LIMB_ONE << (GMP_NUMB_BITS - rw)
: MPFR_LIMB_ONE);
yp[0] &= himask;
return carry;
#endif
}
}
}
else
{
/* Rounding toward zero / no inexact flag */
#if flag == 0
if (MPFR_LIKELY(rw))
{
nw++;
himask = ~MPFR_LIMB_MASK (GMP_NUMB_BITS - rw);
}
else
himask = MPFR_LIMB_MAX;
mpn_copyi (yp, xp + xsize - nw, nw);
yp[0] &= himask;
#endif
return 0;
}
}
#undef flag
#undef use_inexp
#undef mpfr_round_raw_generic