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/* mpfr_set_z_2exp -- set a floating-point number from a multiple-precision
integer and an exponent
Copyright 1999-2021 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"
/* 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;
int k, sign_z, inex;
mp_limb_t *fp, *zp;
mpfr_exp_t exp, nmax;
mpfr_uexp_t uexp;
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 = ABSIZ(z); /* limb size of z */
MPFR_ASSERTD (zn >= 1);
nmax = MPFR_EMAX_MAX / GMP_NUMB_BITS + 1;
/* Detect early overflow with zn + en > nmax,
where en = floor(e / GMP_NUMB_BITS).
This is checked without an integer overflow (even assuming some
future version of GMP, where limitations may be removed). */
if (MPFR_UNLIKELY (e >= 0 ?
zn > nmax - e / GMP_NUMB_BITS :
zn + (e + 1) / GMP_NUMB_BITS - 1 > nmax))
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 */
/* We need to compute exp = zn * GMP_NUMB_BITS + e - k with well-defined
operations (no integer overflows / no implementation-defined results).
The mathematical result of zn * GMP_NUMB_BITS may be larger than
the largest value of mpfr_exp_t while exp could still be less than
__gmpfr_emax. Thanks to early overflow detection, we can compute the
result in modular arithmetic, using mpfr_uexp_t, and convert it to
mpfr_exp_t. */
uexp = (mpfr_uexp_t) zn * GMP_NUMB_BITS + (mpfr_uexp_t) e - k;
/* Convert to signed in a portable way (see doc/README.dev).
On most platforms, this can be optimized to identity (no-op). */
exp = uexp > MPFR_EXP_MAX ? -1 - (mpfr_exp_t) ~uexp : (mpfr_exp_t) uexp;
/* 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_UNLIKELY (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_UNLIKELY (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 && 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 = - ((sb | rb) != 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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