efee5258bc
The MPFR library is a C library for multiple-precision floating-point computations with exact rounding (also called correct rounding). It is based on the GMP multiple-precision library and should replace the MPF class in further releases of GMP. GCC >= 4.2 requires MPFR.
260 lines
8.1 KiB
C
260 lines
8.1 KiB
C
/* mpfr_round_raw_generic -- Generic rounding function
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Copyright 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011 Free Software Foundation, Inc.
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Contributed by the Arenaire and Cacao projects, INRIA.
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This file is part of the GNU MPFR Library.
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The GNU MPFR Library is free software; you can redistribute it and/or modify
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it under the terms of the GNU Lesser General Public License as published by
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the Free Software Foundation; either version 3 of the License, or (at your
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option) any later version.
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The GNU MPFR Library is distributed in the hope that it will be useful, but
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WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
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License for more details.
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You should have received a copy of the GNU Lesser General Public License
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along with the GNU MPFR Library; see the file COPYING.LESSER. If not, see
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http://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc.,
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51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */
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#ifndef flag
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# error "ERROR: flag must be defined (0 / 1)"
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#endif
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#ifndef use_inexp
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# error "ERROR: use_enexp must be defined (0 / 1)"
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#endif
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#ifndef mpfr_round_raw_generic
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# error "ERROR: mpfr_round_raw_generic must be defined"
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#endif
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/*
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* If flag = 0, puts in y the value of xp (with precision xprec and
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* sign 1 if negative=0, -1 otherwise) rounded to precision yprec and
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* direction rnd_mode. Supposes x is not zero nor NaN nor +/- Infinity
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* (i.e. *xp != 0). In that case, the return value is a possible carry
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* (0 or 1) that may happen during the rounding, in which case the result
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* is a power of two.
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*
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* If inexp != NULL, put in *inexp the inexact flag of the rounding (0, 1, -1).
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* In case of even rounding when rnd = MPFR_RNDN, put MPFR_EVEN_INEX (2) or
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* -MPFR_EVEN_INEX (-2) in *inexp.
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*
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* If flag = 1, just returns whether one should add 1 or not for rounding.
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*
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* Note: yprec may be < MPFR_PREC_MIN; in particular, it may be equal
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* to 1. In this case, the even rounding is done away from 0, which is
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* a natural generalization. Indeed, a number with 1-bit precision can
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* be seen as a denormalized number with more precision.
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*/
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int
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mpfr_round_raw_generic(
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#if flag == 0
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mp_limb_t *yp,
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#endif
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const mp_limb_t *xp, mpfr_prec_t xprec,
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int neg, mpfr_prec_t yprec, mpfr_rnd_t rnd_mode
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#if use_inexp != 0
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, int *inexp
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#endif
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)
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{
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mp_size_t xsize, nw;
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mp_limb_t himask, lomask, sb;
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int rw;
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#if flag == 0
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int carry;
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#endif
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#if use_inexp == 0
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int *inexp;
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#endif
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if (use_inexp)
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MPFR_ASSERTD(inexp != ((int*) 0));
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MPFR_ASSERTD(neg == 0 || neg == 1);
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if (flag && !use_inexp &&
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(xprec <= yprec || MPFR_IS_LIKE_RNDZ (rnd_mode, neg)))
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return 0;
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xsize = (xprec-1)/GMP_NUMB_BITS + 1;
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nw = yprec / GMP_NUMB_BITS;
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rw = yprec & (GMP_NUMB_BITS - 1);
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if (MPFR_UNLIKELY(xprec <= yprec))
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{ /* No rounding is necessary. */
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/* if yp=xp, maybe an overlap: MPN_COPY_DECR is ok when src <= dst */
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if (MPFR_LIKELY(rw))
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nw++;
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MPFR_ASSERTD(nw >= 1);
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MPFR_ASSERTD(nw >= xsize);
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if (use_inexp)
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*inexp = 0;
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#if flag == 0
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MPN_COPY_DECR(yp + (nw - xsize), xp, xsize);
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MPN_ZERO(yp, nw - xsize);
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#endif
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return 0;
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}
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if (use_inexp || !MPFR_IS_LIKE_RNDZ(rnd_mode, neg))
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{
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mp_size_t k = xsize - nw - 1;
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if (MPFR_LIKELY(rw))
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{
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nw++;
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lomask = MPFR_LIMB_MASK (GMP_NUMB_BITS - rw);
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himask = ~lomask;
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}
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else
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{
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lomask = ~(mp_limb_t) 0;
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himask = ~(mp_limb_t) 0;
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}
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MPFR_ASSERTD(k >= 0);
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sb = xp[k] & lomask; /* First non-significant bits */
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/* Rounding to nearest ? */
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if (MPFR_LIKELY( rnd_mode == MPFR_RNDN) )
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{
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/* Rounding to nearest */
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mp_limb_t rbmask = MPFR_LIMB_ONE << (GMP_NUMB_BITS - 1 - rw);
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if (sb & rbmask) /* rounding bit */
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sb &= ~rbmask; /* it is 1, clear it */
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else
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{
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/* Rounding bit is 0, behave like rounding to 0 */
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goto rnd_RNDZ;
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}
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while (MPFR_UNLIKELY(sb == 0) && k > 0)
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sb = xp[--k];
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/* rounding to nearest, with rounding bit = 1 */
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if (MPFR_UNLIKELY(sb == 0)) /* Even rounding. */
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{
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/* sb == 0 && rnd_mode == MPFR_RNDN */
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sb = xp[xsize - nw] & (himask ^ (himask << 1));
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if (sb == 0)
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{
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if (use_inexp)
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*inexp = 2*MPFR_EVEN_INEX*neg-MPFR_EVEN_INEX;
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/* ((neg!=0)^(sb!=0)) ? MPFR_EVEN_INEX : -MPFR_EVEN_INEX;*/
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/* Since neg = 0 or 1 and sb=0*/
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#if flag == 1
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return 0 /*sb != 0 && rnd_mode != MPFR_RNDZ */;
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#else
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MPN_COPY_INCR(yp, xp + xsize - nw, nw);
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yp[0] &= himask;
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return 0;
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#endif
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}
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else
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{
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/* sb != 0 && rnd_mode == MPFR_RNDN */
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if (use_inexp)
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*inexp = MPFR_EVEN_INEX-2*MPFR_EVEN_INEX*neg;
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/*((neg!=0)^(sb!=0))? MPFR_EVEN_INEX : -MPFR_EVEN_INEX; */
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/*Since neg= 0 or 1 and sb != 0 */
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goto rnd_RNDN_add_one_ulp;
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}
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}
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else /* sb != 0 && rnd_mode == MPFR_RNDN*/
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{
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if (use_inexp)
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/* *inexp = (neg == 0) ? 1 : -1; but since neg = 0 or 1 */
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*inexp = 1-2*neg;
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rnd_RNDN_add_one_ulp:
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#if flag == 1
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return 1; /*sb != 0 && rnd_mode != MPFR_RNDZ;*/
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#else
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carry = mpn_add_1 (yp, xp + xsize - nw, nw,
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rw ?
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MPFR_LIMB_ONE << (GMP_NUMB_BITS - rw)
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: MPFR_LIMB_ONE);
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yp[0] &= himask;
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return carry;
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#endif
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}
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}
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/* Rounding to Zero ? */
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else if (MPFR_IS_LIKE_RNDZ(rnd_mode, neg))
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{
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/* rnd_mode == MPFR_RNDZ */
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rnd_RNDZ:
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while (MPFR_UNLIKELY(sb == 0) && k > 0)
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sb = xp[--k];
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if (use_inexp)
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/* rnd_mode == MPFR_RNDZ and neg = 0 or 1 */
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/* (neg != 0) ^ (rnd_mode != MPFR_RNDZ)) ? 1 : -1);*/
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*inexp = MPFR_UNLIKELY(sb == 0) ? 0 : (2*neg-1);
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#if flag == 1
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return 0; /*sb != 0 && rnd_mode != MPFR_RNDZ;*/
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#else
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MPN_COPY_INCR(yp, xp + xsize - nw, nw);
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yp[0] &= himask;
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return 0;
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#endif
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}
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else
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{
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/* rnd_mode = Away */
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while (MPFR_UNLIKELY(sb == 0) && k > 0)
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sb = xp[--k];
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if (MPFR_UNLIKELY(sb == 0))
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{
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/* sb = 0 && rnd_mode != MPFR_RNDZ */
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if (use_inexp)
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/* (neg != 0) ^ (rnd_mode != MPFR_RNDZ)) ? 1 : -1);*/
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*inexp = 0;
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#if flag == 1
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return 0;
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#else
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MPN_COPY_INCR(yp, xp + xsize - nw, nw);
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yp[0] &= himask;
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return 0;
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#endif
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}
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else
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{
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/* sb != 0 && rnd_mode != MPFR_RNDZ */
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if (use_inexp)
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/* (neg != 0) ^ (rnd_mode != MPFR_RNDZ)) ? 1 : -1);*/
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*inexp = 1-2*neg;
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#if flag == 1
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return 1;
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#else
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carry = mpn_add_1(yp, xp + xsize - nw, nw,
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rw ? MPFR_LIMB_ONE << (GMP_NUMB_BITS - rw)
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: 1);
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yp[0] &= himask;
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return carry;
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#endif
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}
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}
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}
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else
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{
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/* Roundind mode = Zero / No inexact flag */
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#if flag == 1
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return 0 /*sb != 0 && rnd_mode != MPFR_RNDZ*/;
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#else
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if (MPFR_LIKELY(rw))
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{
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nw++;
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himask = ~MPFR_LIMB_MASK (GMP_NUMB_BITS - rw);
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}
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else
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himask = ~(mp_limb_t) 0;
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MPN_COPY_INCR(yp, xp + xsize - nw, nw);
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yp[0] &= himask;
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return 0;
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#endif
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}
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}
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#undef flag
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#undef use_inexp
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#undef mpfr_round_raw_generic
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