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/* mpfr_subnormalize -- Subnormalize a floating point number
emulating sub-normal numbers.
Copyright 2005, 2006, 2007, 2008, 2009, 2010 Free Software Foundation, Inc.
Contributed by the Arenaire and Cacao 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
http://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"
/* For MPFR_RNDN, we can have a problem of double rounding.
In such a case, this table helps to conclude what to do (y positive):
Rounding Bit | Sticky Bit | inexact | Action | new inexact
0 | ? | ? | Trunc | sticky
1 | 0 | 1 | Trunc |
1 | 0 | 0 | Trunc if even |
1 | 0 | -1 | AddOneUlp |
1 | 1 | ? | AddOneUlp |
For other rounding mode, there isn't such a problem.
Just round it again and merge the inexact flags.
*/
int
mpfr_subnormalize (mpfr_ptr y, int old_inexact, mpfr_rnd_t rnd)
{
int inexact = 0;
/* The subnormal exponent range are from:
mpfr_emin to mpfr_emin + MPFR_PREC(y) - 1 */
if (MPFR_LIKELY (MPFR_IS_SINGULAR (y)
|| (MPFR_GET_EXP (y) >=
__gmpfr_emin + (mp_exp_t) MPFR_PREC (y) - 1)))
inexact = old_inexact;
/* We have to emulate one bit rounding if EXP(y) = emin */
else if (MPFR_GET_EXP (y) == __gmpfr_emin)
{
/* If this is a power of 2, we don't need rounding.
It handles cases when rouding away and y=0.1*2^emin */
if (mpfr_powerof2_raw (y))
inexact = old_inexact;
/* We keep the same sign for y.
Assuming Y is the real value and y the approximation
and since y is not a power of 2: 0.5*2^emin < Y < 1*2^emin
We also know the direction of the error thanks to inexact flag */
else if (rnd == MPFR_RNDN)
{
mp_limb_t *mant, rb ,sb;
mp_size_t s;
/* We need the rounding bit and the sticky bit. Read them
and use the previous table to conclude. */
s = MPFR_LIMB_SIZE (y) - 1;
mant = MPFR_MANT (y) + s;
rb = *mant & (MPFR_LIMB_HIGHBIT >> 1);
if (rb == 0)
goto set_min;
sb = *mant & ((MPFR_LIMB_HIGHBIT >> 1) - 1);
while (sb == 0 && s-- != 0)
sb = *--mant;
if (sb != 0)
goto set_min_p1;
/* Rounding bit is 1 and sticky bit is 0.
We need to examine old inexact flag to conclude. */
if ((old_inexact > 0 && MPFR_SIGN (y) > 0) ||
(old_inexact < 0 && MPFR_SIGN (y) < 0))
goto set_min;
/* If inexact != 0, return 0.1*2^(emin+1).
Otherwise, rounding bit = 1, sticky bit = 0 and inexact = 0
So we have 0.1100000000000000000000000*2^emin exactly.
We return 0.1*2^(emin+1) according to the even-rounding
rule on subnormals. */
goto set_min_p1;
}
else if (MPFR_IS_LIKE_RNDZ (rnd, MPFR_IS_NEG (y)))
{
set_min:
mpfr_setmin (y, __gmpfr_emin);
inexact = -MPFR_SIGN (y);
}
else
{
set_min_p1:
/* Note: mpfr_setmin will abort if __gmpfr_emax == __gmpfr_emin. */
mpfr_setmin (y, __gmpfr_emin + 1);
inexact = MPFR_SIGN (y);
}
}
else /* Hard case: It is more or less the same problem than mpfr_cache */
{
mpfr_t dest;
mpfr_prec_t q;
int sign;
/* Compute the intermediary precision */
q = (mpfr_uexp_t) MPFR_GET_EXP (y) - __gmpfr_emin + 1;
mpfr_init2 (dest, q);
/* Round y in dest */
sign = MPFR_SIGN (y);
MPFR_SET_EXP (dest, MPFR_GET_EXP (y));
MPFR_SET_SIGN (dest, sign);
MPFR_RNDRAW_EVEN (inexact, dest,
MPFR_MANT (y), MPFR_PREC (y), rnd, sign,
MPFR_SET_EXP (dest, MPFR_GET_EXP (dest)+1));
if (MPFR_LIKELY (old_inexact != 0))
{
if (MPFR_UNLIKELY(rnd == MPFR_RNDN && (inexact == MPFR_EVEN_INEX
|| inexact == -MPFR_EVEN_INEX)))
{
/* if both roundings are in the same direction, we have to go
back in the other direction */
if (SAME_SIGN (inexact, old_inexact))
{
if (SAME_SIGN (inexact, MPFR_INT_SIGN (y)))
mpfr_nexttozero (dest);
else
mpfr_nexttoinf (dest);
inexact = -inexact;
}
}
else if (MPFR_UNLIKELY (inexact == 0))
inexact = old_inexact;
}
old_inexact = mpfr_set (y, dest, rnd);
MPFR_ASSERTN (old_inexact == 0);
MPFR_ASSERTN (MPFR_IS_PURE_FP (y));
mpfr_clear (dest);
}
return inexact;
}
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