/* mpfr_set_d -- convert a machine double precision float to
a multiple precision floating-point number
Copyright 1999-2004, 2006-2023 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 <float.h> /* For DOUBLE_ISINF and DOUBLE_ISNAN */
#define MPFR_NEED_LONGLONG_H
#include "mpfr-impl.h"
/* Extracts the bits of |d| in rp[0..n-1] where n=ceil(53/GMP_NUMB_BITS).
Assumes d finite and <> 0.
Returns the corresponding exponent such that |d| = {rp, n} * 2^exp,
with the value of {rp, n} in [1/2, 1).
The int type should be sufficient for exp.
*/
static int
extract_double (mpfr_limb_ptr rp, double d)
{
int exp;
mp_limb_t man[MPFR_LIMBS_PER_DOUBLE];
/* FIXME: Generalize to handle GMP_NUMB_BITS < 16. */
MPFR_ASSERTD(!DOUBLE_ISNAN(d));
MPFR_ASSERTD(!DOUBLE_ISINF(d));
MPFR_ASSERTD(d != 0.0);
#if _MPFR_IEEE_FLOATS
{
union mpfr_ieee_double_extract x;
x.d = d;
exp = x.s.exp;
if (exp)
{
/* x.s.manh has 20 bits (in its low bits), x.s.manl has 32 bits */
#if GMP_NUMB_BITS >= 64
man[0] = ((MPFR_LIMB_ONE << (GMP_NUMB_BITS - 1)) |
((mp_limb_t) x.s.manh << (GMP_NUMB_BITS - 21)) |
((mp_limb_t) x.s.manl << (GMP_NUMB_BITS - 53)));
#elif GMP_NUMB_BITS == 32
man[1] = (MPFR_LIMB_ONE << 31) | (x.s.manh << 11) | (x.s.manl >> 21);
man[0] = x.s.manl << 11;
#elif GMP_NUMB_BITS == 16
MPFR_STAT_STATIC_ASSERT (GMP_NUMB_BITS == 16);
man[3] = (MPFR_LIMB_ONE << 15) | (x.s.manh >> 5);
man[2] = (x.s.manh << 11) | (x.s.manl >> 21);
man[1] = x.s.manl >> 5;
man[0] = MPFR_LIMB_LSHIFT(x.s.manl,11);
#else
MPFR_STAT_STATIC_ASSERT (GMP_NUMB_BITS == 8);
man[6] = (MPFR_LIMB_ONE << 7) | (x.s.manh >> 13);
man[5] = (mp_limb_t) (x.s.manh >> 5);
man[4] = MPFR_LIMB_LSHIFT(x.s.manh, 3) | (mp_limb_t) (x.s.manl >> 29);
man[3] = (mp_limb_t) (x.s.manl >> 21);
man[2] = (mp_limb_t) (x.s.manl >> 13);
man[1] = (mp_limb_t) (x.s.manl >> 5);
man[0] = MPFR_LIMB_LSHIFT(x.s.manl,3);
#endif
exp -= 1022;
}
else /* subnormal number */
{
int cnt;
exp = -1021;
#if GMP_NUMB_BITS >= 64
man[0] = (((mp_limb_t) x.s.manh << (GMP_NUMB_BITS - 21)) |
((mp_limb_t) x.s.manl << (GMP_NUMB_BITS - 53)));
count_leading_zeros (cnt, man[0]);
#elif GMP_NUMB_BITS == 32
man[1] = (x.s.manh << 11) /* high 21 bits */
| (x.s.manl >> 21); /* middle 11 bits */
man[0] = x.s.manl << 11; /* low 21 bits */
if (man[1] == 0)
{
man[1] = man[0];
man[0] = 0;
exp -= GMP_NUMB_BITS;
}
count_leading_zeros (cnt, man[1]);
man[1] = (man[1] << cnt) |
(cnt != 0 ? man[0] >> (GMP_NUMB_BITS - cnt) : 0);
#elif GMP_NUMB_BITS == 16
man[3] = x.s.manh >> 5;
man[2] = (x.s.manh << 11) | (x.s.manl >> 21);
man[1] = x.s.manl >> 5;
man[0] = x.s.manl << 11;
while (man[3] == 0) /* d is assumed <> 0 */
{
man[3] = man[2];
man[2] = man[1];
man[1] = man[0];
man[0] = 0;
exp -= GMP_NUMB_BITS;
}
count_leading_zeros (cnt, man[3]);
if (cnt)
{
man[3] = (man[3] << cnt) | (man[2] >> (GMP_NUMB_BITS - cnt));
man[2] = (man[2] << cnt) | (man[1] >> (GMP_NUMB_BITS - cnt));
man[1] = (man[1] << cnt) | (man[0] >> (GMP_NUMB_BITS - cnt));
}
#else
MPFR_STAT_STATIC_ASSERT (GMP_NUMB_BITS == 8);
man[6] = x.s.manh >> 13;
man[5] = x.s.manh >> 5;
man[4] = (x.s.manh << 3) | (x.s.manl >> 29);
man[3] = x.s.manl >> 21;
man[2] = x.s.manl >> 13;
man[1] = x.s.manl >> 5;
man[0] = x.s.manl << 3;
while (man[6] == 0) /* d is assumed <> 0 */
{
man[6] = man[5];
man[5] = man[4];
man[4] = man[3];
man[3] = man[2];
man[2] = man[1];
man[1] = man[0];
man[0] = 0;
exp -= GMP_NUMB_BITS;
}
count_leading_zeros (cnt, man[6]);
if (cnt)
{
int i;
for (i = 6; i > 0; i--)
man[i] = (man[i] << cnt) | (man[i-1] >> (GMP_NUMB_BITS - cnt));
}
#endif
man[0] <<= cnt;
exp -= cnt;
}
}
#else /* _MPFR_IEEE_FLOATS */
{
/* Unknown (or known to be non-IEEE) double format. */
exp = 0;
d = ABS (d);
if (d >= 1.0)
{
while (d >= 32768.0)
{
d *= (1.0 / 65536.0);
exp += 16;
}
while (d >= 1.0)
{
d *= 0.5;
exp += 1;
}
}
else if (d < 0.5)
{
while (d < (1.0 / 65536.0))
{
d *= 65536.0;
exp -= 16;
}
while (d < 0.5)
{
d *= 2.0;
exp -= 1;
}
}
d *= MP_BASE_AS_DOUBLE;
#if GMP_NUMB_BITS >= 64
#ifndef __clang__
man[0] = d;
#else
/* clang up to version 11 produces an invalid exception when d >= 2^63,
see <https://github.com/llvm/llvm-project/issues/18060>
(old URL: <https://bugs.llvm.org/show_bug.cgi?id=17686>).
Since this is always the case, here, we use the following patch. */
MPFR_STAT_STATIC_ASSERT (GMP_NUMB_BITS == 64);
man[0] = 0x8000000000000000 + (mp_limb_t) (d - 0x8000000000000000);
#endif /* __clang__ */
#elif GMP_NUMB_BITS == 32
man[1] = (mp_limb_t) d;
man[0] = (mp_limb_t) ((d - man[1]) * MP_BASE_AS_DOUBLE);
#else
MPFR_STAT_STATIC_ASSERT (GMP_NUMB_BITS == 16);
{
double r = d;
man[3] = (mp_limb_t) r;
r = (r - man[3]) * MP_BASE_AS_DOUBLE;
man[2] = (mp_limb_t) r;
r = (r - man[2]) * MP_BASE_AS_DOUBLE;
man[1] = (mp_limb_t) r;
r = (r - man[1]) * MP_BASE_AS_DOUBLE;
man[0] = (mp_limb_t) r;
}
#endif
}
#endif /* _MPFR_IEEE_FLOATS */
rp[0] = man[0];
#if GMP_NUMB_BITS <= 32
rp[1] = man[1];
#endif
#if GMP_NUMB_BITS <= 16
rp[2] = man[2];
rp[3] = man[3];
#endif
#if GMP_NUMB_BITS <= 8
rp[4] = man[4];
rp[5] = man[5];
rp[6] = man[6];
#endif
MPFR_ASSERTD((rp[MPFR_LIMBS_PER_DOUBLE - 1] & MPFR_LIMB_HIGHBIT) != 0);
return exp;
}
/* End of part included from gmp-2.0.2 */
int
mpfr_set_d (mpfr_ptr r, double d, mpfr_rnd_t rnd_mode)
{
int inexact;
mpfr_t tmp;
mp_limb_t tmpmant[MPFR_LIMBS_PER_DOUBLE];
MPFR_SAVE_EXPO_DECL (expo);
if (MPFR_UNLIKELY(DOUBLE_ISNAN(d)))
{
/* we don't propagate the sign bit */
MPFR_SET_NAN(r);
MPFR_RET_NAN;
}
else if (MPFR_UNLIKELY(d == 0))
{
#if _MPFR_IEEE_FLOATS
union mpfr_ieee_double_extract x;
MPFR_SET_ZERO(r);
/* set correct sign */
x.d = d;
if (x.s.sig == 1)
MPFR_SET_NEG(r);
else
MPFR_SET_POS(r);
#else /* _MPFR_IEEE_FLOATS */
MPFR_SET_ZERO(r);
{
/* This is to get the sign of zero on non-IEEE hardware
Some systems support +0.0, -0.0, and unsigned zero.
Some other systems may just have an unsigned zero.
We can't use d == +0.0 since it should be always true,
so we check that the memory representation of d is the
same as +0.0, etc.
Note: r is set to -0 only if d is detected as a negative zero
*and*, for the double type, -0 has a different representation
from +0. If -0.0 has several representations, the code below
may not work as expected, but this is hardly fixable in a
portable way (without depending on a math library) and only
the sign could be incorrect. Such systems should be taken
into account on a case-by-case basis. If the code is changed
here, set_d64.c code should be updated too. */
double poszero = +0.0, negzero = DBL_NEG_ZERO;
if (memcmp(&d, &poszero, sizeof(double)) == 0)
MPFR_SET_POS(r);
else if (memcmp(&d, &negzero, sizeof(double)) == 0)
MPFR_SET_NEG(r);
else
MPFR_SET_POS(r);
}
#endif /* _MPFR_IEEE_FLOATS */
return 0; /* 0 is exact */
}
else if (MPFR_UNLIKELY(DOUBLE_ISINF(d)))
{
MPFR_SET_INF(r);
if (d > 0)
MPFR_SET_POS(r);
else
MPFR_SET_NEG(r);
return 0; /* infinity is exact */
}
/* now d is neither 0, nor NaN nor Inf */
MPFR_SAVE_EXPO_MARK (expo);
/* warning: don't use tmp=r here, even if SIZE(r) >= MPFR_LIMBS_PER_DOUBLE,
since PREC(r) may be different from PREC(tmp), and then both variables
would have same precision in the mpfr_set4 call below. */
MPFR_MANT(tmp) = tmpmant;
MPFR_PREC(tmp) = IEEE_DBL_MANT_DIG;
/* don't use MPFR_SET_EXP here since the exponent may be out of range */
MPFR_EXP(tmp) = extract_double (tmpmant, d);
/* tmp is exact since PREC(tmp)=53 */
inexact = mpfr_set4 (r, tmp, rnd_mode,
(d < 0) ? MPFR_SIGN_NEG : MPFR_SIGN_POS);
MPFR_SAVE_EXPO_FREE (expo);
return mpfr_check_range (r, inexact, rnd_mode);
}