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/* mpfr_set -- copy of a floating-point number
Copyright 1999, 2001-2021 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. */
#include "mpfr-impl.h"
/* set a to abs(b) * signb: a=b when signb = SIGN(b), a=abs(b) when signb=1 */
MPFR_HOT_FUNCTION_ATTR int
mpfr_set4 (mpfr_ptr a, mpfr_srcptr b, mpfr_rnd_t rnd_mode, int signb)
{
/* Sign is ALWAYS copied */
MPFR_SET_SIGN (a, signb);
/* Exponent is also always copied since if the number is singular,
the exponent field determined the number.
Can't use MPFR_SET_EXP since the exponent may be singular */
MPFR_EXP (a) = MPFR_EXP (b);
if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (b)))
{
/* MPFR_SET_NAN, MPFR_SET_ZERO and MPFR_SET_INF are useless
since MPFR_EXP (a) = MPFR_EXP (b) does the job */
if (MPFR_IS_NAN (b))
MPFR_RET_NAN;
else
MPFR_RET (0);
}
else if (MPFR_PREC (b) == MPFR_PREC (a))
{
/* Same precision and b is not singular:
* just copy the mantissa, and set the exponent and the sign
* The result is exact. */
MPN_COPY (MPFR_MANT (a), MPFR_MANT (b), MPFR_LIMB_SIZE (b));
MPFR_RET (0);
}
else
{
int inex;
/* Else Round B inside a */
MPFR_RNDRAW (inex, a, MPFR_MANT (b), MPFR_PREC (b), rnd_mode, signb,
if (MPFR_UNLIKELY (++ MPFR_EXP (a) > __gmpfr_emax))
return mpfr_overflow (a, rnd_mode, signb)
);
MPFR_RET (inex);
}
}
/* Set a to b */
#undef mpfr_set
int
mpfr_set (mpfr_ptr a, mpfr_srcptr b, mpfr_rnd_t rnd_mode)
{
/* Contrary to other mpfr_set4 based functions (mpfr_abs, mpfr_neg, etc.),
do not detect the case a == b as there is no interest to call mpfr_set
in this case, so that it is very unlikely that the user calls it
with a == b (this is the reverse of what is assumed for the other
functions). */
return mpfr_set4 (a, b, rnd_mode, MPFR_SIGN (b));
}
/* Set a to |b| */
#undef mpfr_abs
int
mpfr_abs (mpfr_ptr a, mpfr_srcptr b, mpfr_rnd_t rnd_mode)
{
if (MPFR_UNLIKELY (a != b))
return mpfr_set4 (a, b, rnd_mode, MPFR_SIGN_POS);
else
{
MPFR_SET_POS (a);
if (MPFR_UNLIKELY (MPFR_IS_NAN (b)))
MPFR_RET_NAN;
else
MPFR_RET (0);
}
}
/* Round (u, inex) into s with rounding mode rnd_mode, where inex is
the ternary value associated with u, which has been obtained using
the *same* rounding mode rnd_mode.
Assumes PREC(u) = 2*PREC(s).
The generic algorithm is the following:
1. inex2 = mpfr_set (s, u, rnd_mode);
2. if (inex2 != 0) return inex2; else return inex;
except in the double-rounding case: in MPFR_RNDN, when u is in the
middle of two consecutive PREC(s)-bit numbers, if inex and inex2
are both > 0 (resp. both < 0), we correct s to nextbelow(s) (resp.
nextabove(s)), and return the opposite of inex.
Note: this function can be called with rnd_mode == MPFR_RNDF, in
which case, the rounding direction and the returned ternary value
are unspecified. */
int
mpfr_set_1_2 (mpfr_ptr s, mpfr_srcptr u, mpfr_rnd_t rnd_mode, int inex)
{
mpfr_prec_t p = MPFR_PREC(s);
mpfr_prec_t sh = GMP_NUMB_BITS - p;
mp_limb_t rb, sb;
mp_limb_t *sp = MPFR_MANT(s);
mp_limb_t *up = MPFR_MANT(u);
mp_limb_t mask;
int inex2;
if (MPFR_UNLIKELY(MPFR_IS_SINGULAR(u)))
{
mpfr_set (s, u, rnd_mode);
return inex;
}
MPFR_ASSERTD(MPFR_PREC(u) == 2 * p);
if (p < GMP_NUMB_BITS)
{
mask = MPFR_LIMB_MASK(sh);
if (MPFR_PREC(u) <= GMP_NUMB_BITS)
{
mp_limb_t u0 = up[0];
/* it suffices to round (u0, inex) */
rb = u0 & (MPFR_LIMB_ONE << (sh - 1));
sb = (u0 & mask) ^ rb;
sp[0] = u0 & ~mask;
}
else
{
mp_limb_t u1 = up[1];
/* we need to round (u1, u0, inex) */
mask = MPFR_LIMB_MASK(sh);
rb = u1 & (MPFR_LIMB_ONE << (sh - 1));
sb = ((u1 & mask) ^ rb) | up[0];
sp[0] = u1 & ~mask;
}
inex2 = inex * MPFR_SIGN(u);
MPFR_SIGN(s) = MPFR_SIGN(u);
MPFR_EXP(s) = MPFR_EXP(u);
/* in case inex2 > 0, the value of u is rounded away,
thus we need to subtract something from (u0, rb, sb):
(a) if sb is not zero, since the subtracted value is < 1, we can leave
sb as it is;
(b) if rb <> 0 and sb = 0: change to rb = 0 and sb = 1
(c) if rb = sb = 0: change to rb = 1 and sb = 1, and subtract 1 */
if (inex2 > 0)
{
if (rb && sb == 0)
{
rb = 0;
sb = 1;
}
}
else /* inex2 <= 0 */
sb |= inex;
/* now rb, sb are the round and sticky bits, together with the value of
sp[0], except possibly in the case rb = sb = 0 and inex2 > 0 */
if (rb == 0 && sb == 0)
{
if (inex2 <= 0)
MPFR_RET(0);
else /* inex2 > 0 can only occur for RNDN and RNDA:
RNDN: return sp[0] and inex
RNDA: return sp[0] and inex */
MPFR_RET(inex);
}
else if (rnd_mode == MPFR_RNDN)
{
if (rb == 0 || (sb == 0 && (sp[0] & (MPFR_LIMB_ONE << sh)) == 0))
goto truncate;
else
goto add_one_ulp;
}
else if (MPFR_IS_LIKE_RNDZ(rnd_mode, MPFR_IS_NEG(s)))
{
truncate:
MPFR_RET(-MPFR_SIGN(s));
}
else /* round away from zero */
{
add_one_ulp:
sp[0] += MPFR_LIMB_ONE << sh;
if (MPFR_UNLIKELY(sp[0] == 0))
{
sp[0] = MPFR_LIMB_HIGHBIT;
if (MPFR_EXP(s) + 1 <= __gmpfr_emax)
MPFR_SET_EXP (s, MPFR_EXP(s) + 1);
else /* overflow */
return mpfr_overflow (s, rnd_mode, MPFR_SIGN(s));
}
MPFR_RET(MPFR_SIGN(s));
}
}
/* general case PREC(s) >= GMP_NUMB_BITS */
inex2 = mpfr_set (s, u, rnd_mode);
/* Check the double-rounding case, i.e. with u = middle of two
consecutive PREC(s)-bit numbers, which is equivalent to u being
exactly representable on PREC(s) + 1 bits but not on PREC(s) bits.
Moreover, since PREC(u) = 2*PREC(s), u and s cannot be identical
(as pointers), thus u was not changed. */
if (rnd_mode == MPFR_RNDN && inex * inex2 > 0 &&
mpfr_min_prec (u) == p + 1)
{
if (inex > 0)
mpfr_nextbelow (s);
else
mpfr_nextabove (s);
return -inex;
}
return inex2 != 0 ? inex2 : inex;
}
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