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/* mpfr_rint -- Round to an integer.
Copyright 1999-2020 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. */
#include "mpfr-impl.h"
/* Merge the following mpfr_rint code with mpfr_round_raw_generic? */
/* For all the round-to-integer functions, we don't need to extend the
* exponent range. And it is better not to do so, so that we can test
* the flag setting for intermediate overflow in the test suite without
* involving huge non-integer numbers (thus in huge precision). This
* should also be faster.
*
* We also need to be careful with the flags.
*/
int
mpfr_rint (mpfr_ptr r, mpfr_srcptr u, mpfr_rnd_t rnd_mode)
{
int sign;
int rnd_away;
mpfr_exp_t exp;
if (MPFR_UNLIKELY( MPFR_IS_SINGULAR(u) ))
{
if (MPFR_IS_NAN(u))
{
MPFR_SET_NAN(r);
MPFR_RET_NAN;
}
MPFR_SET_SAME_SIGN(r, u);
if (MPFR_IS_INF(u))
{
MPFR_SET_INF(r);
MPFR_RET(0); /* infinity is exact */
}
else /* now u is zero */
{
MPFR_ASSERTD(MPFR_IS_ZERO(u));
MPFR_SET_ZERO(r);
MPFR_RET(0); /* zero is exact */
}
}
MPFR_SET_SAME_SIGN (r, u); /* Does nothing if r==u */
sign = MPFR_INT_SIGN (u);
exp = MPFR_GET_EXP (u);
rnd_away =
rnd_mode == MPFR_RNDD ? sign < 0 :
rnd_mode == MPFR_RNDU ? sign > 0 :
rnd_mode == MPFR_RNDZ ? 0 :
rnd_mode == MPFR_RNDA ? 1 :
-1; /* round to nearest-even (RNDN) or nearest-away (RNDNA) */
/* rnd_away:
1 if round away from zero,
0 if round to zero,
-1 if not decided yet.
*/
if (MPFR_UNLIKELY (exp <= 0)) /* 0 < |u| < 1 ==> round |u| to 0 or 1 */
{
/* Note: in the MPFR_RNDN mode, 0.5 must be rounded to 0. */
if (rnd_away != 0 &&
(rnd_away > 0 ||
(exp == 0 && (rnd_mode == MPFR_RNDNA ||
!mpfr_powerof2_raw (u)))))
{
/* The flags will correctly be set and overflow will correctly
be handled by mpfr_set_si. */
mpfr_set_si (r, sign, rnd_mode);
MPFR_RET(sign > 0 ? 2 : -2);
}
else
{
MPFR_SET_ZERO(r); /* r = 0 */
MPFR_RET(sign > 0 ? -2 : 2);
}
}
else /* exp > 0, |u| >= 1 */
{
mp_limb_t *up, *rp;
mp_size_t un, rn, ui;
int sh, idiff;
int uflags;
/*
* uflags will contain:
* _ 0 if u is an integer representable in r,
* _ 1 if u is an integer not representable in r,
* _ 2 if u is not an integer.
*/
up = MPFR_MANT(u);
rp = MPFR_MANT(r);
un = MPFR_LIMB_SIZE(u);
rn = MPFR_LIMB_SIZE(r);
MPFR_UNSIGNED_MINUS_MODULO (sh, MPFR_PREC (r));
/* exp is in the current exponent range: obtained from the input. */
MPFR_SET_EXP (r, exp); /* Does nothing if r==u */
if ((exp - 1) / GMP_NUMB_BITS >= un)
{
ui = un;
idiff = 0;
uflags = 0; /* u is an integer, representable or not in r */
}
else
{
mp_size_t uj;
ui = (exp - 1) / GMP_NUMB_BITS + 1; /* #limbs of the int part */
MPFR_ASSERTD (un >= ui);
uj = un - ui; /* lowest limb of the integer part */
idiff = exp % GMP_NUMB_BITS; /* #int-part bits in up[uj] or 0 */
uflags = idiff == 0 || MPFR_LIMB_LSHIFT(up[uj],idiff) == 0 ? 0 : 2;
if (uflags == 0)
while (uj > 0)
if (up[--uj] != 0)
{
uflags = 2;
break;
}
}
if (ui > rn)
{
/* More limbs in the integer part of u than in r.
Just round u with the precision of r. */
MPFR_ASSERTD (rp != up && un > rn);
MPN_COPY (rp, up + (un - rn), rn); /* r != u */
if (rnd_away < 0)
{
/* This is a rounding to nearest mode (MPFR_RNDN or MPFR_RNDNA).
Decide the rounding direction here. */
if (rnd_mode == MPFR_RNDN &&
(rp[0] & (MPFR_LIMB_ONE << sh)) == 0)
{ /* halfway cases rounded toward zero */
mp_limb_t a, b;
/* a: rounding bit and some of the following bits */
/* b: boundary for a (weight of the rounding bit in a) */
if (sh != 0)
{
a = rp[0] & ((MPFR_LIMB_ONE << sh) - 1);
b = MPFR_LIMB_ONE << (sh - 1);
}
else
{
a = up[un - rn - 1];
b = MPFR_LIMB_HIGHBIT;
}
rnd_away = a > b;
if (a == b)
{
mp_size_t i;
for (i = un - rn - 1 - (sh == 0); i >= 0; i--)
if (up[i] != 0)
{
rnd_away = 1;
break;
}
}
}
else /* halfway cases rounded away from zero */
rnd_away = /* rounding bit */
((sh != 0 && (rp[0] & (MPFR_LIMB_ONE << (sh - 1))) != 0) ||
(sh == 0 && (up[un - rn - 1] & MPFR_LIMB_HIGHBIT) != 0));
}
if (uflags == 0)
{ /* u is an integer; determine if it is representable in r */
if (sh != 0 && MPFR_LIMB_LSHIFT(rp[0], GMP_NUMB_BITS - sh) != 0)
uflags = 1; /* u is not representable in r */
else
{
mp_size_t i;
for (i = un - rn - 1; i >= 0; i--)
if (up[i] != 0)
{
uflags = 1; /* u is not representable in r */
break;
}
}
}
}
else /* ui <= rn */
{
mp_size_t uj, rj;
int ush;
uj = un - ui; /* lowest limb of the integer part in u */
rj = rn - ui; /* lowest limb of the integer part in r */
if (rp != up)
MPN_COPY(rp + rj, up + uj, ui);
/* Ignore the lowest rj limbs, all equal to zero. */
rp += rj;
rn = ui;
/* number of fractional bits in whole rp[0] */
ush = idiff == 0 ? 0 : GMP_NUMB_BITS - idiff;
if (rj == 0 && ush < sh)
{
/* If u is an integer (uflags == 0), we need to determine
if it is representable in r, i.e. if its sh - ush bits
in the non-significant part of r are all 0. */
if (uflags == 0 && (rp[0] & ((MPFR_LIMB_ONE << sh) -
(MPFR_LIMB_ONE << ush))) != 0)
uflags = 1; /* u is an integer not representable in r */
}
else /* The integer part of u fits in r, we'll round to it. */
sh = ush;
if (rnd_away < 0)
{
/* This is a rounding to nearest mode.
Decide the rounding direction here. */
if (uj == 0 && sh == 0)
rnd_away = 0; /* rounding bit = 0 (not represented in u) */
else if (rnd_mode == MPFR_RNDN &&
(rp[0] & (MPFR_LIMB_ONE << sh)) == 0)
{ /* halfway cases rounded toward zero */
mp_limb_t a, b;
/* a: rounding bit and some of the following bits */
/* b: boundary for a (weight of the rounding bit in a) */
if (sh != 0)
{
a = rp[0] & ((MPFR_LIMB_ONE << sh) - 1);
b = MPFR_LIMB_ONE << (sh - 1);
}
else
{
MPFR_ASSERTD (uj >= 1); /* see above */
a = up[uj - 1];
b = MPFR_LIMB_HIGHBIT;
}
rnd_away = a > b;
if (a == b)
{
mp_size_t i;
for (i = uj - 1 - (sh == 0); i >= 0; i--)
if (up[i] != 0)
{
rnd_away = 1;
break;
}
}
}
else /* halfway cases rounded away from zero */
rnd_away = /* rounding bit */
((sh != 0 && (rp[0] & (MPFR_LIMB_ONE << (sh - 1))) != 0) ||
(sh == 0 && (MPFR_ASSERTD (uj >= 1),
up[uj - 1] & MPFR_LIMB_HIGHBIT) != 0));
}
/* Now we can make the low rj limbs to 0 */
MPN_ZERO (rp-rj, rj);
}
if (sh != 0)
rp[0] &= MPFR_LIMB_MAX << sh;
/* If u is a representable integer, there is no rounding. */
if (uflags == 0)
MPFR_RET(0);
MPFR_ASSERTD (rnd_away >= 0); /* rounding direction is defined */
if (rnd_away && mpn_add_1 (rp, rp, rn, MPFR_LIMB_ONE << sh))
{
if (exp == __gmpfr_emax)
return mpfr_overflow (r, rnd_mode, sign) >= 0 ?
uflags : -uflags;
else /* no overflow */
{
MPFR_SET_EXP(r, exp + 1);
rp[rn-1] = MPFR_LIMB_HIGHBIT;
}
}
MPFR_RET (rnd_away ^ (sign < 0) ? uflags : -uflags);
} /* exp > 0, |u| >= 1 */
}
#undef mpfr_roundeven
int
mpfr_roundeven (mpfr_ptr r, mpfr_srcptr u)
{
return mpfr_rint (r, u, MPFR_RNDN);
}
#undef mpfr_round
int
mpfr_round (mpfr_ptr r, mpfr_srcptr u)
{
return mpfr_rint (r, u, MPFR_RNDNA);
}
#undef mpfr_trunc
int
mpfr_trunc (mpfr_ptr r, mpfr_srcptr u)
{
return mpfr_rint (r, u, MPFR_RNDZ);
}
#undef mpfr_ceil
int
mpfr_ceil (mpfr_ptr r, mpfr_srcptr u)
{
return mpfr_rint (r, u, MPFR_RNDU);
}
#undef mpfr_floor
int
mpfr_floor (mpfr_ptr r, mpfr_srcptr u)
{
return mpfr_rint (r, u, MPFR_RNDD);
}
/* We need to save the flags and restore them after calling the mpfr_round,
* mpfr_trunc, mpfr_ceil, mpfr_floor functions because these functions set
* the inexact flag when the argument is not an integer.
*/
#undef mpfr_rint_roundeven
int
mpfr_rint_roundeven (mpfr_ptr r, mpfr_srcptr u, mpfr_rnd_t rnd_mode)
{
if (MPFR_UNLIKELY( MPFR_IS_SINGULAR(u) ) || mpfr_integer_p (u))
return mpfr_set (r, u, rnd_mode);
else
{
mpfr_t tmp;
int inex;
mpfr_flags_t saved_flags = __gmpfr_flags;
MPFR_BLOCK_DECL (flags);
mpfr_init2 (tmp, MPFR_PREC (u));
/* round(u) is representable in tmp unless an overflow occurs */
MPFR_BLOCK (flags, mpfr_roundeven (tmp, u));
__gmpfr_flags = saved_flags;
inex = (MPFR_OVERFLOW (flags)
? mpfr_overflow (r, rnd_mode, MPFR_SIGN (u))
: mpfr_set (r, tmp, rnd_mode));
mpfr_clear (tmp);
return inex;
}
}
#undef mpfr_rint_round
int
mpfr_rint_round (mpfr_ptr r, mpfr_srcptr u, mpfr_rnd_t rnd_mode)
{
if (MPFR_UNLIKELY( MPFR_IS_SINGULAR(u) ) || mpfr_integer_p (u))
return mpfr_set (r, u, rnd_mode);
else
{
mpfr_t tmp;
int inex;
mpfr_flags_t saved_flags = __gmpfr_flags;
MPFR_BLOCK_DECL (flags);
mpfr_init2 (tmp, MPFR_PREC (u));
/* round(u) is representable in tmp unless an overflow occurs */
MPFR_BLOCK (flags, mpfr_round (tmp, u));
__gmpfr_flags = saved_flags;
inex = (MPFR_OVERFLOW (flags)
? mpfr_overflow (r, rnd_mode, MPFR_SIGN (u))
: mpfr_set (r, tmp, rnd_mode));
mpfr_clear (tmp);
return inex;
}
}
#undef mpfr_rint_trunc
int
mpfr_rint_trunc (mpfr_ptr r, mpfr_srcptr u, mpfr_rnd_t rnd_mode)
{
if (MPFR_UNLIKELY( MPFR_IS_SINGULAR(u) ) || mpfr_integer_p (u))
return mpfr_set (r, u, rnd_mode);
else
{
mpfr_t tmp;
int inex;
mpfr_flags_t saved_flags = __gmpfr_flags;
mpfr_init2 (tmp, MPFR_PREC (u));
/* trunc(u) is always representable in tmp */
mpfr_trunc (tmp, u);
__gmpfr_flags = saved_flags;
inex = mpfr_set (r, tmp, rnd_mode);
mpfr_clear (tmp);
return inex;
}
}
#undef mpfr_rint_ceil
int
mpfr_rint_ceil (mpfr_ptr r, mpfr_srcptr u, mpfr_rnd_t rnd_mode)
{
if (MPFR_UNLIKELY( MPFR_IS_SINGULAR(u) ) || mpfr_integer_p (u))
return mpfr_set (r, u, rnd_mode);
else
{
mpfr_t tmp;
int inex;
mpfr_flags_t saved_flags = __gmpfr_flags;
MPFR_BLOCK_DECL (flags);
mpfr_init2 (tmp, MPFR_PREC (u));
/* ceil(u) is representable in tmp unless an overflow occurs */
MPFR_BLOCK (flags, mpfr_ceil (tmp, u));
__gmpfr_flags = saved_flags;
inex = (MPFR_OVERFLOW (flags)
? mpfr_overflow (r, rnd_mode, MPFR_SIGN_POS)
: mpfr_set (r, tmp, rnd_mode));
mpfr_clear (tmp);
return inex;
}
}
#undef mpfr_rint_floor
int
mpfr_rint_floor (mpfr_ptr r, mpfr_srcptr u, mpfr_rnd_t rnd_mode)
{
if (MPFR_UNLIKELY( MPFR_IS_SINGULAR(u) ) || mpfr_integer_p (u))
return mpfr_set (r, u, rnd_mode);
else
{
mpfr_t tmp;
int inex;
mpfr_flags_t saved_flags = __gmpfr_flags;
MPFR_BLOCK_DECL (flags);
mpfr_init2 (tmp, MPFR_PREC (u));
/* floor(u) is representable in tmp unless an overflow occurs */
MPFR_BLOCK (flags, mpfr_floor (tmp, u));
__gmpfr_flags = saved_flags;
inex = (MPFR_OVERFLOW (flags)
? mpfr_overflow (r, rnd_mode, MPFR_SIGN_NEG)
: mpfr_set (r, tmp, rnd_mode));
mpfr_clear (tmp);
return inex;
}
}
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