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/* Split a double into fraction and mantissa.
Copyright (C) 2007-2020 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/>. */
/* Written by Paolo Bonzini <bonzini@gnu.org>, 2003, and
Bruno Haible <bruno@clisp.org>, 2007. */
#if ! defined USE_LONG_DOUBLE
# include <config.h>
#endif
/* Specification. */
#include <math.h>
#include <float.h>
#ifdef USE_LONG_DOUBLE
# include "isnanl-nolibm.h"
# include "fpucw.h"
#else
# include "isnand-nolibm.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 <= 1.0, not < 1.0. */
#ifdef USE_LONG_DOUBLE
# define FUNC frexpl
# define DOUBLE long double
# define ISNAN isnanl
# 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 frexp
# define DOUBLE double
# define ISNAN isnand
# define DECL_ROUNDING
# define BEGIN_ROUNDING()
# define END_ROUNDING()
# define L_(literal) literal
#endif
DOUBLE
FUNC (DOUBLE x, int *expptr)
{
int sign;
int exponent;
DECL_ROUNDING
/* Test for NaN, infinity, and zero. */
if (ISNAN (x) || x + x == x)
{
*expptr = 0;
return x;
}
sign = 0;
if (x < 0)
{
x = - x;
sign = -1;
}
BEGIN_ROUNDING ();
{
/* 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 positive 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;
}
/* Avoid making x too small, as it could become a denormalized
number and thus lose precision. */
while (i > 0 && x < pow2[i - 1])
{
i--;
powh_i = powh[i];
}
exponent += (1 << i);
x *= powh_i;
/* Here 2^-2^i <= x < 1.0. */
}
else
{
/* A negative or zero 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 < powh_i)
{
exponent -= (1 << i);
x *= pow2_i;
}
else
break;
pow2[i] = pow2_i;
powh[i] = powh_i;
}
/* Here 2^-2^i <= x < 1.0. */
}
/* Invariants: x * 2^exponent = argument, and 2^-2^i <= x < 1.0. */
while (i > 0)
{
i--;
if (x < powh[i])
{
exponent -= (1 << i);
x *= pow2[i];
}
}
/* Here 0.5 <= x < 1.0. */
}
if (sign < 0)
x = - x;
END_ROUNDING ();
*expptr = exponent;
return x;
}
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