efee5258bc
The MPFR library is a C library for multiple-precision floating-point computations with exact rounding (also called correct rounding). It is based on the GMP multiple-precision library and should replace the MPF class in further releases of GMP. GCC >= 4.2 requires MPFR.
256 lines
6.7 KiB
C
256 lines
6.7 KiB
C
/* mpfr_set_d -- convert a machine double precision float to
|
|
a multiple precision floating-point number
|
|
|
|
Copyright 1999, 2000, 2001, 2002, 2003, 2004, 2006, 2007, 2008, 2009, 2010, 2011 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 <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 is neither 0 nor NaN nor Inf. */
|
|
static long
|
|
__gmpfr_extract_double (mpfr_limb_ptr rp, double d)
|
|
/* e=0 iff GMP_NUMB_BITS=32 and rp has only one limb */
|
|
{
|
|
long exp;
|
|
mp_limb_t manl;
|
|
#if GMP_NUMB_BITS == 32
|
|
mp_limb_t manh;
|
|
#endif
|
|
|
|
/* BUGS
|
|
1. Should handle Inf and NaN in IEEE specific code.
|
|
2. Handle Inf and NaN also in default code, to avoid hangs.
|
|
3. Generalize to handle all GMP_NUMB_BITS.
|
|
4. This lits is incomplete and misspelled.
|
|
*/
|
|
|
|
MPFR_ASSERTD(!DOUBLE_ISNAN(d));
|
|
MPFR_ASSERTD(!DOUBLE_ISINF(d));
|
|
MPFR_ASSERTD(d != 0.0);
|
|
|
|
#if _GMP_IEEE_FLOATS
|
|
|
|
{
|
|
union ieee_double_extract x;
|
|
x.d = d;
|
|
|
|
exp = x.s.exp;
|
|
if (exp)
|
|
{
|
|
#if GMP_NUMB_BITS >= 64
|
|
manl = ((MPFR_LIMB_ONE << 63)
|
|
| ((mp_limb_t) x.s.manh << 43) | ((mp_limb_t) x.s.manl << 11));
|
|
#else
|
|
manh = (MPFR_LIMB_ONE << 31) | (x.s.manh << 11) | (x.s.manl >> 21);
|
|
manl = x.s.manl << 11;
|
|
#endif
|
|
}
|
|
else /* denormalized number */
|
|
{
|
|
#if GMP_NUMB_BITS >= 64
|
|
manl = ((mp_limb_t) x.s.manh << 43) | ((mp_limb_t) x.s.manl << 11);
|
|
#else
|
|
manh = (x.s.manh << 11) /* high 21 bits */
|
|
| (x.s.manl >> 21); /* middle 11 bits */
|
|
manl = x.s.manl << 11; /* low 21 bits */
|
|
#endif
|
|
}
|
|
|
|
if (exp)
|
|
exp -= 1022;
|
|
else
|
|
exp = -1021;
|
|
}
|
|
|
|
#else /* _GMP_IEEE_FLOATS */
|
|
|
|
{
|
|
/* Unknown (or known to be non-IEEE) double format. */
|
|
exp = 0;
|
|
if (d >= 1.0)
|
|
{
|
|
MPFR_ASSERTN (d * 0.5 != d);
|
|
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
|
|
manl = d;
|
|
#else
|
|
manh = (mp_limb_t) d;
|
|
manl = (mp_limb_t) ((d - manh) * MP_BASE_AS_DOUBLE);
|
|
#endif
|
|
}
|
|
|
|
#endif /* _GMP_IEEE_FLOATS */
|
|
|
|
#if GMP_NUMB_BITS >= 64
|
|
rp[0] = manl;
|
|
#else
|
|
rp[1] = manh;
|
|
rp[0] = manl;
|
|
#endif
|
|
|
|
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 signd, inexact;
|
|
unsigned int cnt;
|
|
mp_size_t i, k;
|
|
mpfr_t tmp;
|
|
mp_limb_t tmpmant[MPFR_LIMBS_PER_DOUBLE];
|
|
MPFR_SAVE_EXPO_DECL (expo);
|
|
|
|
if (MPFR_UNLIKELY(DOUBLE_ISNAN(d)))
|
|
{
|
|
MPFR_SET_NAN(r);
|
|
MPFR_RET_NAN;
|
|
}
|
|
else if (MPFR_UNLIKELY(d == 0))
|
|
{
|
|
#if _GMP_IEEE_FLOATS
|
|
union 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 /* _GMP_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.
|
|
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 than +0.0. etc */
|
|
/* FIXME: consider the case where +0.0 or -0.0 may have several
|
|
representations. */
|
|
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
|
|
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;
|
|
|
|
signd = (d < 0) ? MPFR_SIGN_NEG : MPFR_SIGN_POS;
|
|
d = ABS (d);
|
|
|
|
/* don't use MPFR_SET_EXP here since the exponent may be out of range */
|
|
MPFR_EXP(tmp) = __gmpfr_extract_double (tmpmant, d);
|
|
|
|
#ifdef WANT_ASSERT
|
|
/* Failed assertion if the stored value is 0 (e.g., if the exponent range
|
|
has been reduced at the wrong moment and an underflow to 0 occurred).
|
|
Probably a bug in the C implementation if this happens. */
|
|
i = 0;
|
|
while (tmpmant[i] == 0)
|
|
{
|
|
i++;
|
|
MPFR_ASSERTN(i < MPFR_LIMBS_PER_DOUBLE);
|
|
}
|
|
#endif
|
|
|
|
/* determine the index i-1 of the most significant non-zero limb
|
|
and the number k of zero high limbs */
|
|
i = MPFR_LIMBS_PER_DOUBLE;
|
|
MPN_NORMALIZE_NOT_ZERO(tmpmant, i);
|
|
k = MPFR_LIMBS_PER_DOUBLE - i;
|
|
|
|
count_leading_zeros (cnt, tmpmant[i - 1]);
|
|
|
|
if (MPFR_LIKELY(cnt != 0))
|
|
mpn_lshift (tmpmant + k, tmpmant, i, cnt);
|
|
else if (k != 0)
|
|
MPN_COPY (tmpmant + k, tmpmant, i);
|
|
|
|
if (MPFR_UNLIKELY(k != 0))
|
|
MPN_ZERO (tmpmant, k);
|
|
|
|
/* don't use MPFR_SET_EXP here since the exponent may be out of range */
|
|
MPFR_EXP(tmp) -= (mpfr_exp_t) (cnt + k * GMP_NUMB_BITS);
|
|
|
|
/* tmp is exact since PREC(tmp)=53 */
|
|
inexact = mpfr_set4 (r, tmp, rnd_mode, signd);
|
|
|
|
MPFR_SAVE_EXPO_FREE (expo);
|
|
return mpfr_check_range (r, inexact, rnd_mode);
|
|
}
|
|
|
|
|
|
|