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/* Split a double into fraction and mantissa, for hexadecimal printf.
Copyright (C) 2007, 2009-2020 Free Software Foundation, Inc.
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 3 of the License, or
(at your option) any later version.
This program 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 General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see <https://www.gnu.org/licenses/>. */
#if ! defined USE_LONG_DOUBLE
# include <config.h>
#endif
/* Specification. */
#ifdef USE_LONG_DOUBLE
# include "printf-frexpl.h"
#else
# include "printf-frexp.h"
#endif
#include <float.h>
#include <math.h>
#ifdef USE_LONG_DOUBLE
# include "fpucw.h"
#endif
/* This file assumes FLT_RADIX = 2. If FLT_RADIX is a power of 2 greater
than 2, or not even a power of 2, some rounding errors can occur, so that
then the returned mantissa is only guaranteed to be <= 2.0, not < 2.0. */
#ifdef USE_LONG_DOUBLE
# define FUNC printf_frexpl
# define DOUBLE long double
# define MIN_EXP LDBL_MIN_EXP
# if HAVE_FREXPL_IN_LIBC && HAVE_LDEXPL_IN_LIBC
# define USE_FREXP_LDEXP
# define FREXP frexpl
# define LDEXP ldexpl
# endif
# define DECL_ROUNDING DECL_LONG_DOUBLE_ROUNDING
# define BEGIN_ROUNDING() BEGIN_LONG_DOUBLE_ROUNDING ()
# define END_ROUNDING() END_LONG_DOUBLE_ROUNDING ()
# define L_(literal) literal##L
#else
# define FUNC printf_frexp
# define DOUBLE double
# define MIN_EXP DBL_MIN_EXP
# if HAVE_FREXP_IN_LIBC && HAVE_LDEXP_IN_LIBC
# define USE_FREXP_LDEXP
# define FREXP frexp
# define LDEXP ldexp
# endif
# define DECL_ROUNDING
# define BEGIN_ROUNDING()
# define END_ROUNDING()
# define L_(literal) literal
#endif
DOUBLE
FUNC (DOUBLE x, int *expptr)
{
int exponent;
DECL_ROUNDING
BEGIN_ROUNDING ();
#ifdef USE_FREXP_LDEXP
/* frexp and ldexp are usually faster than the loop below. */
x = FREXP (x, &exponent);
x = x + x;
exponent -= 1;
if (exponent < MIN_EXP - 1)
{
x = LDEXP (x, exponent - (MIN_EXP - 1));
exponent = MIN_EXP - 1;
}
#else
{
/* Since the exponent is an 'int', it fits in 64 bits. Therefore the
loops are executed no more than 64 times. */
DOUBLE pow2[64]; /* pow2[i] = 2^2^i */
DOUBLE powh[64]; /* powh[i] = 2^-2^i */
int i;
exponent = 0;
if (x >= L_(1.0))
{
/* A nonnegative exponent. */
{
DOUBLE pow2_i; /* = pow2[i] */
DOUBLE powh_i; /* = powh[i] */
/* Invariants: pow2_i = 2^2^i, powh_i = 2^-2^i,
x * 2^exponent = argument, x >= 1.0. */
for (i = 0, pow2_i = L_(2.0), powh_i = L_(0.5);
;
i++, pow2_i = pow2_i * pow2_i, powh_i = powh_i * powh_i)
{
if (x >= pow2_i)
{
exponent += (1 << i);
x *= powh_i;
}
else
break;
pow2[i] = pow2_i;
powh[i] = powh_i;
}
}
/* Here 1.0 <= x < 2^2^i. */
}
else
{
/* A negative exponent. */
{
DOUBLE pow2_i; /* = pow2[i] */
DOUBLE powh_i; /* = powh[i] */
/* Invariants: pow2_i = 2^2^i, powh_i = 2^-2^i,
x * 2^exponent = argument, x < 1.0, exponent >= MIN_EXP - 1. */
for (i = 0, pow2_i = L_(2.0), powh_i = L_(0.5);
;
i++, pow2_i = pow2_i * pow2_i, powh_i = powh_i * powh_i)
{
if (exponent - (1 << i) < MIN_EXP - 1)
break;
exponent -= (1 << i);
x *= pow2_i;
if (x >= L_(1.0))
break;
pow2[i] = pow2_i;
powh[i] = powh_i;
}
}
/* Here either x < 1.0 and exponent - 2^i < MIN_EXP - 1 <= exponent,
or 1.0 <= x < 2^2^i and exponent >= MIN_EXP - 1. */
if (x < L_(1.0))
/* Invariants: x * 2^exponent = argument, x < 1.0 and
exponent - 2^i < MIN_EXP - 1 <= exponent. */
while (i > 0)
{
i--;
if (exponent - (1 << i) >= MIN_EXP - 1)
{
exponent -= (1 << i);
x *= pow2[i];
if (x >= L_(1.0))
break;
}
}
/* Here either x < 1.0 and exponent = MIN_EXP - 1,
or 1.0 <= x < 2^2^i and exponent >= MIN_EXP - 1. */
}
/* Invariants: x * 2^exponent = argument, and
either x < 1.0 and exponent = MIN_EXP - 1,
or 1.0 <= x < 2^2^i and exponent >= MIN_EXP - 1. */
while (i > 0)
{
i--;
if (x >= pow2[i])
{
exponent += (1 << i);
x *= powh[i];
}
}
/* Here either x < 1.0 and exponent = MIN_EXP - 1,
or 1.0 <= x < 2.0 and exponent >= MIN_EXP - 1. */
}
#endif
END_ROUNDING ();
*expptr = exponent;
return x;
}
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