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/* mpfr_set_z_2exp -- set a floating-point number from a multiple-precision
integer and an exponent
Copyright 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010 Free Software Foundation, Inc.
Contributed by the Arenaire and Caramel 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. */
#define MPFR_NEED_LONGLONG_H
#include "mpfr-impl.h"
/* set f to the integer z multiplied by 2^e */
int
mpfr_set_z_2exp (mpfr_ptr f, mpz_srcptr z, mpfr_exp_t e, mpfr_rnd_t rnd_mode)
{
mp_size_t fn, zn, dif, en;
int k, sign_z, inex;
mp_limb_t *fp, *zp;
mpfr_exp_t exp;
sign_z = mpz_sgn (z);
if (MPFR_UNLIKELY (sign_z == 0)) /* ignore the exponent for 0 */
{
MPFR_SET_ZERO(f);
MPFR_SET_POS(f);
MPFR_RET(0);
}
MPFR_ASSERTD (sign_z == MPFR_SIGN_POS || sign_z == MPFR_SIGN_NEG);
zn = ABS(SIZ(z)); /* limb size of z */
/* compute en = floor(e/GMP_NUMB_BITS) */
en = (e >= 0) ? e / GMP_NUMB_BITS : (e + 1) / GMP_NUMB_BITS - 1;
MPFR_ASSERTD (zn >= 1);
if (MPFR_UNLIKELY (zn + en > MPFR_EMAX_MAX / GMP_NUMB_BITS + 1))
return mpfr_overflow (f, rnd_mode, sign_z);
/* because zn + en >= MPFR_EMAX_MAX / GMP_NUMB_BITS + 2
implies (zn + en) * GMP_NUMB_BITS >= MPFR_EMAX_MAX + GMP_NUMB_BITS + 1
and exp = zn * GMP_NUMB_BITS + e - k
>= (zn + en) * GMP_NUMB_BITS - k > MPFR_EMAX_MAX */
fp = MPFR_MANT (f);
fn = MPFR_LIMB_SIZE (f);
dif = zn - fn;
zp = PTR(z);
count_leading_zeros (k, zp[zn-1]);
/* now zn + en <= MPFR_EMAX_MAX / GMP_NUMB_BITS + 1
thus (zn + en) * GMP_NUMB_BITS <= MPFR_EMAX_MAX + GMP_NUMB_BITS
and exp = zn * GMP_NUMB_BITS + e - k
<= (zn + en) * GMP_NUMB_BITS - k + GMP_NUMB_BITS - 1
<= MPFR_EMAX_MAX + 2 * GMP_NUMB_BITS - 1 */
exp = (mpfr_prec_t) zn * GMP_NUMB_BITS + e - k;
/* The exponent will be exp or exp + 1 (due to rounding) */
if (MPFR_UNLIKELY (exp > __gmpfr_emax))
return mpfr_overflow (f, rnd_mode, sign_z);
if (MPFR_UNLIKELY (exp + 1 < __gmpfr_emin))
return mpfr_underflow (f, rnd_mode == MPFR_RNDN ? MPFR_RNDZ : rnd_mode,
sign_z);
if (MPFR_LIKELY (dif >= 0))
{
mp_limb_t rb, sb, ulp;
int sh;
/* number has to be truncated */
if (MPFR_LIKELY (k != 0))
{
mpn_lshift (fp, &zp[dif], fn, k);
if (MPFR_LIKELY (dif > 0))
fp[0] |= zp[dif - 1] >> (GMP_NUMB_BITS - k);
}
else
MPN_COPY (fp, zp + dif, fn);
/* Compute Rounding Bit and Sticky Bit */
MPFR_UNSIGNED_MINUS_MODULO (sh, MPFR_PREC (f) );
if (MPFR_LIKELY (sh != 0))
{
mp_limb_t mask = MPFR_LIMB_ONE << (sh-1);
mp_limb_t limb = fp[0];
rb = limb & mask;
sb = limb & (mask-1);
ulp = 2*mask;
fp[0] = limb & ~(ulp-1);
}
else /* sh == 0 */
{
mp_limb_t mask = MPFR_LIMB_ONE << (GMP_NUMB_BITS - 1 - k);
if (MPFR_LIKELY (dif > 0))
{
rb = zp[--dif] & mask;
sb = zp[dif] & (mask-1);
}
else
rb = sb = 0;
k = 0;
ulp = MPFR_LIMB_ONE;
}
if (MPFR_UNLIKELY (sb == 0) && MPFR_LIKELY (dif > 0))
{
sb = zp[--dif];
if (MPFR_LIKELY (k != 0))
sb &= MPFR_LIMB_MASK (GMP_NUMB_BITS - k);
if (MPFR_UNLIKELY (sb == 0) && MPFR_LIKELY (dif > 0))
do {
sb = zp[--dif];
} while (dif > 0 && sb == 0);
}
/* Rounding */
if (MPFR_LIKELY (rnd_mode == MPFR_RNDN))
{
if (rb == 0 || MPFR_UNLIKELY (sb == 0 && (fp[0] & ulp) == 0))
goto trunc;
else
goto addoneulp;
}
else /* Not Nearest */
{
if (MPFR_LIKELY (MPFR_IS_LIKE_RNDZ (rnd_mode, sign_z < 0))
|| MPFR_UNLIKELY ( (sb | rb) == 0 ))
goto trunc;
else
goto addoneulp;
}
trunc:
inex = MPFR_LIKELY ((sb | rb) != 0) ? -1 : 0;
goto end;
addoneulp:
inex = 1;
if (MPFR_UNLIKELY (mpn_add_1 (fp, fp, fn, ulp)))
{
/* Pow 2 case */
if (MPFR_UNLIKELY (exp == __gmpfr_emax))
return mpfr_overflow (f, rnd_mode, sign_z);
exp ++;
fp[fn-1] = MPFR_LIMB_HIGHBIT;
}
end:
(void) 0;
}
else /* dif < 0: Mantissa F is strictly bigger than z's one */
{
if (MPFR_LIKELY (k != 0))
mpn_lshift (fp - dif, zp, zn, k);
else
MPN_COPY (fp - dif, zp, zn);
/* fill with zeroes */
MPN_ZERO (fp, -dif);
inex = 0; /* result is exact */
}
if (MPFR_UNLIKELY (exp < __gmpfr_emin))
{
if (rnd_mode == MPFR_RNDN && inex == 0 && mpfr_powerof2_raw (f))
rnd_mode = MPFR_RNDZ;
return mpfr_underflow (f, rnd_mode, sign_z);
}
MPFR_SET_EXP (f, exp);
MPFR_SET_SIGN (f, sign_z);
MPFR_RET (inex*sign_z);
}
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