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/* mpfr_frac -- Fractional part of a floating-point number.
Copyright 2002-2004, 2006-2019 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. */
#define MPFR_NEED_LONGLONG_H
#include "mpfr-impl.h"
/* Optimization note: it is not a good idea to call mpfr_integer_p,
as some cases will take longer (the number may be parsed twice). */
int
mpfr_frac (mpfr_ptr r, mpfr_srcptr u, mpfr_rnd_t rnd_mode)
{
mpfr_exp_t re, ue;
mpfr_prec_t uq;
mp_size_t un, tn, t0;
mp_limb_t *up, *tp, k;
int sh;
mpfr_t tmp;
mpfr_ptr t;
int inex;
MPFR_SAVE_EXPO_DECL (expo);
/* Special cases */
if (MPFR_UNLIKELY(MPFR_IS_NAN(u)))
{
MPFR_SET_NAN(r);
MPFR_RET_NAN;
}
else if (MPFR_UNLIKELY(MPFR_IS_INF(u) || mpfr_integer_p (u)))
{
MPFR_SET_SAME_SIGN(r, u);
MPFR_SET_ZERO(r);
MPFR_RET(0); /* zero is exact */
}
ue = MPFR_GET_EXP (u);
if (ue <= 0) /* |u| < 1 */
return mpfr_set (r, u, rnd_mode);
/* Now |u| >= 1, meaning that an overflow is not possible. */
uq = MPFR_PREC(u);
un = (uq - 1) / GMP_NUMB_BITS; /* index of most significant limb */
un -= (mp_size_t) (ue / GMP_NUMB_BITS);
/* now the index of the MSL containing bits of the fractional part */
up = MPFR_MANT(u);
sh = ue % GMP_NUMB_BITS;
k = up[un] << sh;
/* the first bit of the fractional part is the MSB of k */
if (k != 0)
{
int cnt;
count_leading_zeros(cnt, k);
/* first bit 1 of the fractional part -> MSB of the number */
re = -cnt;
sh += cnt;
MPFR_ASSERTN (sh < GMP_NUMB_BITS);
k <<= cnt;
}
else
{
re = sh - GMP_NUMB_BITS;
/* searching for the first bit 1 (exists since u isn't an integer) */
while (up[--un] == 0)
re -= GMP_NUMB_BITS;
MPFR_ASSERTN(un >= 0);
k = up[un];
count_leading_zeros(sh, k);
re -= sh;
k <<= sh;
}
/* The exponent of r will be re */
/* un: index of the limb of u that contains the first bit 1 of the FP */
t = (mp_size_t) (MPFR_PREC(r) - 1) / GMP_NUMB_BITS < un ?
(mpfr_init2 (tmp, (un + 1) * GMP_NUMB_BITS), tmp) : r;
/* t has enough precision to contain the fractional part of u */
/* If we use a temporary variable, we take the non-significant bits
of u into account, because of the mpn_lshift below. */
MPFR_SET_SAME_SIGN(t, u);
/* Put the fractional part of u into t */
tn = (MPFR_PREC(t) - 1) / GMP_NUMB_BITS;
MPFR_ASSERTN(tn >= un);
t0 = tn - un;
tp = MPFR_MANT(t);
if (sh == 0)
mpn_copyd (tp + t0, up, un + 1);
else /* warning: un may be 0 here */
tp[tn] = k | ((un) ? mpn_lshift (tp + t0, up, un, sh) : MPFR_LIMB_ZERO);
if (t0 > 0)
MPN_ZERO(tp, t0);
MPFR_SAVE_EXPO_MARK (expo);
if (t != r)
{ /* t is tmp */
MPFR_EXP (t) = 0; /* should be re, but not necessarily in the range */
inex = mpfr_set (r, t, rnd_mode); /* no underflow */
mpfr_clear (t);
MPFR_EXP (r) += re;
}
else
{ /* There may be remaining non-significant bits in t (= r). */
int carry;
MPFR_EXP (r) = re;
carry = mpfr_round_raw (tp, tp,
(mpfr_prec_t) (tn + 1) * GMP_NUMB_BITS,
MPFR_IS_NEG (r), MPFR_PREC (r), rnd_mode,
&inex);
if (carry)
{
tp[tn] = MPFR_LIMB_HIGHBIT;
MPFR_EXP (r) ++;
}
}
MPFR_SAVE_EXPO_FREE (expo);
return mpfr_check_range (r, inex, rnd_mode);
}
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