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/* mpfr_set_ld -- convert a machine long double to
a multiple precision floating-point number
Copyright 2002-2020 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> /* needed so that MPFR_LDBL_MANT_DIG is correctly defined */
#define MPFR_NEED_LONGLONG_H
#include "mpfr-impl.h"
/* To check for +inf, one can use the test x > LDBL_MAX, as LDBL_MAX is
the maximum finite number representable in a long double, according
to DR 467; see
http://www.open-std.org/jtc1/sc22/wg14/www/docs/n2092.htm
If this fails on some platform, a test x - x != 0 might be used. */
#if defined(HAVE_LDOUBLE_IS_DOUBLE)
/* the "long double" format is the same as "double" */
int
mpfr_set_ld (mpfr_ptr r, long double d, mpfr_rnd_t rnd_mode)
{
return mpfr_set_d (r, (double) d, rnd_mode);
}
#elif defined(HAVE_LDOUBLE_IEEE_EXT_LITTLE)
#if GMP_NUMB_BITS >= 64
# define MPFR_LIMBS_PER_LONG_DOUBLE 1
#elif GMP_NUMB_BITS == 32
# define MPFR_LIMBS_PER_LONG_DOUBLE 2
#elif GMP_NUMB_BITS == 16
# define MPFR_LIMBS_PER_LONG_DOUBLE 4
#elif GMP_NUMB_BITS == 8
# define MPFR_LIMBS_PER_LONG_DOUBLE 8
#else
#error "GMP_NUMB_BITS is assumed to be 8, 16, 32 or >= 64"
#endif
/* The hypothetical GMP_NUMB_BITS == 16 is not supported. It will trigger
an error below. */
/* IEEE Extended Little Endian Code */
int
mpfr_set_ld (mpfr_ptr r, long double d, mpfr_rnd_t rnd_mode)
{
int inexact, k, cnt;
mpfr_t tmp;
mp_limb_t tmpmant[MPFR_LIMBS_PER_LONG_DOUBLE];
mpfr_long_double_t x;
mpfr_exp_t exp;
int signd;
MPFR_SAVE_EXPO_DECL (expo);
/* Check for NAN */
if (MPFR_UNLIKELY (DOUBLE_ISNAN (d)))
{
MPFR_SET_NAN (r);
MPFR_RET_NAN;
}
/* Check for INF */
else if (MPFR_UNLIKELY (d > LDBL_MAX))
{
MPFR_SET_INF (r);
MPFR_SET_POS (r);
return 0;
}
else if (MPFR_UNLIKELY (d < -LDBL_MAX))
{
MPFR_SET_INF (r);
MPFR_SET_NEG (r);
return 0;
}
/* Check for ZERO */
else if (MPFR_UNLIKELY (d == 0.0))
{
x.ld = d;
MPFR_SET_ZERO (r);
if (x.s.sign == 1)
MPFR_SET_NEG(r);
else
MPFR_SET_POS(r);
return 0;
}
/* now d is neither 0, nor NaN nor Inf */
MPFR_SAVE_EXPO_MARK (expo);
MPFR_MANT (tmp) = tmpmant;
MPFR_PREC (tmp) = 64;
/* Extract sign */
x.ld = d;
signd = MPFR_SIGN_POS;
if (x.ld < 0.0)
{
signd = MPFR_SIGN_NEG;
x.ld = -x.ld;
}
/* Extract and normalize the significand */
#if MPFR_LIMBS_PER_LONG_DOUBLE == 1
tmpmant[0] = ((mp_limb_t) x.s.manh << 32) | ((mp_limb_t) x.s.manl);
count_leading_zeros (cnt, tmpmant[0]);
tmpmant[0] <<= cnt;
k = 0; /* number of limbs shifted */
#else /* MPFR_LIMBS_PER_LONG_DOUBLE >= 2 */
#if MPFR_LIMBS_PER_LONG_DOUBLE == 2
tmpmant[0] = (mp_limb_t) x.s.manl;
tmpmant[1] = (mp_limb_t) x.s.manh;
#elif MPFR_LIMBS_PER_LONG_DOUBLE == 4
tmpmant[0] = (mp_limb_t) x.s.manl;
tmpmant[1] = (mp_limb_t) (x.s.manl >> 16);
tmpmant[2] = (mp_limb_t) x.s.manh;
tmpmant[3] = (mp_limb_t) (x.s.manh >> 16);
#elif MPFR_LIMBS_PER_LONG_DOUBLE == 8
tmpmant[0] = (mp_limb_t) x.s.manl;
tmpmant[1] = (mp_limb_t) (x.s.manl >> 8);
tmpmant[2] = (mp_limb_t) (x.s.manl >> 16);
tmpmant[3] = (mp_limb_t) (x.s.manl >> 24);
tmpmant[4] = (mp_limb_t) x.s.manh;
tmpmant[5] = (mp_limb_t) (x.s.manh >> 8);
tmpmant[6] = (mp_limb_t) (x.s.manh >> 16);
tmpmant[7] = (mp_limb_t) (x.s.manh >> 24);
#else
#error "MPFR_LIMBS_PER_LONG_DOUBLE should be 1, 2, 4 or 8"
#endif /* MPFR_LIMBS_PER_LONG_DOUBLE >= 2 */
{
int i = MPFR_LIMBS_PER_LONG_DOUBLE;
MPN_NORMALIZE_NOT_ZERO (tmpmant, i);
k = MPFR_LIMBS_PER_LONG_DOUBLE - i;
count_leading_zeros (cnt, tmpmant[i - 1]);
if (cnt != 0)
mpn_lshift (tmpmant + k, tmpmant, i, cnt);
else if (k != 0)
/* since we copy {tmpmant, i} into {tmpmant + k, i}, we should work
decreasingly, thus call mpn_copyd */
mpn_copyd (tmpmant + k, tmpmant, i);
if (k != 0)
MPN_ZERO (tmpmant, k);
}
#endif /* MPFR_LIMBS_PER_LONG_DOUBLE == 1 */
/* Set exponent */
exp = (mpfr_exp_t) ((x.s.exph << 8) + x.s.expl); /* 15-bit unsigned int */
if (MPFR_UNLIKELY (exp == 0))
exp -= 0x3FFD;
else
exp -= 0x3FFE;
MPFR_SET_EXP (tmp, exp - cnt - k * GMP_NUMB_BITS);
/* tmp is exact */
inexact = mpfr_set4 (r, tmp, rnd_mode, signd);
MPFR_SAVE_EXPO_FREE (expo);
return mpfr_check_range (r, inexact, rnd_mode);
}
#elif defined(HAVE_LDOUBLE_MAYBE_DOUBLE_DOUBLE)
/* double-double code */
int
mpfr_set_ld (mpfr_ptr r, long double d, mpfr_rnd_t rnd_mode)
{
mpfr_t t, u;
int inexact;
double h, l;
MPFR_SAVE_EXPO_DECL (expo);
/* Check for NAN */
LONGDOUBLE_NAN_ACTION (d, goto nan);
/* Check for INF */
if (d > LDBL_MAX)
{
mpfr_set_inf (r, 1);
return 0;
}
else if (d < -LDBL_MAX)
{
mpfr_set_inf (r, -1);
return 0;
}
/* Check for ZERO */
else if (d == 0.0)
return mpfr_set_d (r, (double) d, rnd_mode);
if (d >= LDBL_MAX || d <= -LDBL_MAX)
h = (d >= LDBL_MAX) ? LDBL_MAX : -LDBL_MAX;
else
h = (double) d; /* should not overflow */
l = (double) (d - (long double) h);
MPFR_SAVE_EXPO_MARK (expo);
mpfr_init2 (t, IEEE_DBL_MANT_DIG);
mpfr_init2 (u, IEEE_DBL_MANT_DIG);
inexact = mpfr_set_d (t, h, MPFR_RNDN);
MPFR_ASSERTN(inexact == 0);
inexact = mpfr_set_d (u, l, MPFR_RNDN);
MPFR_ASSERTN(inexact == 0);
inexact = mpfr_add (r, t, u, rnd_mode);
mpfr_clear (t);
mpfr_clear (u);
MPFR_SAVE_EXPO_FREE (expo);
inexact = mpfr_check_range (r, inexact, rnd_mode);
return inexact;
nan:
MPFR_SET_NAN(r);
MPFR_RET_NAN;
}
#else
/* Generic code */
int
mpfr_set_ld (mpfr_ptr r, long double d, mpfr_rnd_t rnd_mode)
{
mpfr_t t, u;
int inexact, shift_exp;
long double x;
MPFR_SAVE_EXPO_DECL (expo);
/* Check for NAN */
LONGDOUBLE_NAN_ACTION (d, goto nan);
/* Check for INF */
if (d > LDBL_MAX)
{
mpfr_set_inf (r, 1);
return 0;
}
else if (d < -LDBL_MAX)
{
mpfr_set_inf (r, -1);
return 0;
}
/* Check for ZERO */
else if (d == 0.0)
return mpfr_set_d (r, (double) d, rnd_mode);
mpfr_init2 (t, MPFR_LDBL_MANT_DIG);
mpfr_init2 (u, IEEE_DBL_MANT_DIG);
MPFR_SAVE_EXPO_MARK (expo);
convert:
x = d;
MPFR_SET_ZERO (t); /* The sign doesn't matter. */
shift_exp = 0; /* invariant: remainder to deal with is d*2^shift_exp */
while (x != (long double) 0.0)
{
/* Check overflow of double */
if (x > (long double) DBL_MAX || (-x) > (long double) DBL_MAX)
{
long double div9, div10, div11, div12, div13;
#define TWO_64 18446744073709551616.0 /* 2^64 */
#define TWO_128 (TWO_64 * TWO_64)
#define TWO_256 (TWO_128 * TWO_128)
div9 = (long double) (double) (TWO_256 * TWO_256); /* 2^(2^9) */
div10 = div9 * div9;
div11 = div10 * div10; /* 2^(2^11) */
div12 = div11 * div11; /* 2^(2^12) */
div13 = div12 * div12; /* 2^(2^13) */
if (ABS (x) >= div13)
{
x /= div13; /* exact */
shift_exp += 8192;
mpfr_div_2si (t, t, 8192, MPFR_RNDZ);
}
if (ABS (x) >= div12)
{
x /= div12; /* exact */
shift_exp += 4096;
mpfr_div_2si (t, t, 4096, MPFR_RNDZ);
}
if (ABS (x) >= div11)
{
x /= div11; /* exact */
shift_exp += 2048;
mpfr_div_2si (t, t, 2048, MPFR_RNDZ);
}
if (ABS (x) >= div10)
{
x /= div10; /* exact */
shift_exp += 1024;
mpfr_div_2si (t, t, 1024, MPFR_RNDZ);
}
/* warning: we may have DBL_MAX=2^1024*(1-2^(-53)) < x < 2^1024,
therefore we have one extra exponent reduction step */
if (ABS (x) >= div9)
{
x /= div9; /* exact */
shift_exp += 512;
mpfr_div_2si (t, t, 512, MPFR_RNDZ);
}
} /* Check overflow of double */
else /* no overflow on double */
{
long double div9, div10, div11;
div9 = (long double) (double) 7.4583407312002067432909653e-155;
/* div9 = 2^(-2^9) */
div10 = div9 * div9; /* 2^(-2^10) */
div11 = div10 * div10; /* 2^(-2^11) if extended precision */
/* since -DBL_MAX <= x <= DBL_MAX, the cast to double should not
overflow here */
if (ABS(x) < div10 &&
div11 != (long double) 0.0 &&
div11 / div10 == div10) /* possible underflow */
{
long double div12, div13;
/* After the divisions, any bit of x must be >= div10,
hence the possible division by div9. */
div12 = div11 * div11; /* 2^(-2^12) */
div13 = div12 * div12; /* 2^(-2^13) */
if (ABS (x) <= div13)
{
x /= div13; /* exact */
shift_exp -= 8192;
mpfr_mul_2si (t, t, 8192, MPFR_RNDZ);
}
if (ABS (x) <= div12)
{
x /= div12; /* exact */
shift_exp -= 4096;
mpfr_mul_2si (t, t, 4096, MPFR_RNDZ);
}
if (ABS (x) <= div11)
{
x /= div11; /* exact */
shift_exp -= 2048;
mpfr_mul_2si (t, t, 2048, MPFR_RNDZ);
}
if (ABS (x) <= div10)
{
x /= div10; /* exact */
shift_exp -= 1024;
mpfr_mul_2si (t, t, 1024, MPFR_RNDZ);
}
if (ABS(x) <= div9)
{
x /= div9; /* exact */
shift_exp -= 512;
mpfr_mul_2si (t, t, 512, MPFR_RNDZ);
}
}
else /* no underflow */
{
inexact = mpfr_set_d (u, (double) x, MPFR_RNDZ);
MPFR_ASSERTD (inexact == 0);
if (mpfr_add (t, t, u, MPFR_RNDZ) != 0)
{
if (!mpfr_number_p (t))
break;
/* Inexact. This cannot happen unless the C implementation
"lies" on the precision or when long doubles are
implemented with FP expansions like double-double on
PowerPC. */
if (MPFR_PREC (t) != MPFR_PREC (r) + 1)
{
/* We assume that MPFR_PREC (r) < MPFR_PREC_MAX.
The precision MPFR_PREC (r) + 1 allows us to
deduce the rounding bit and the sticky bit. */
mpfr_set_prec (t, MPFR_PREC (r) + 1);
goto convert;
}
else
{
mp_limb_t *tp;
int rb_mask;
/* Since mpfr_add was inexact, the sticky bit is 1. */
tp = MPFR_MANT (t);
rb_mask = MPFR_LIMB_ONE <<
(GMP_NUMB_BITS - 1 -
(MPFR_PREC (r) & (GMP_NUMB_BITS - 1)));
if (rnd_mode == MPFR_RNDN)
rnd_mode = (*tp & rb_mask) ^ MPFR_IS_NEG (t) ?
MPFR_RNDU : MPFR_RNDD;
*tp |= rb_mask;
break;
}
}
x -= (long double) mpfr_get_d1 (u); /* exact */
}
}
}
inexact = mpfr_mul_2si (r, t, shift_exp, rnd_mode);
mpfr_clear (t);
mpfr_clear (u);
MPFR_SAVE_EXPO_FREE (expo);
return mpfr_check_range (r, inexact, rnd_mode);
nan:
MPFR_SET_NAN(r);
MPFR_RET_NAN;
}
#endif
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