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/* Round according to the current rounding mode.
Copyright (C) 2007, 2010-2019 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 2, 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. */
#include <math.h>
#include <float.h>
#include <stdlib.h>
#undef MIN
#ifdef USE_LONG_DOUBLE
# define RINT rintl
# define DOUBLE long double
# define MANT_DIG LDBL_MANT_DIG
# define MIN LDBL_MIN
# define L_(literal) literal##L
#elif ! defined USE_FLOAT
# define RINT rint
# define DOUBLE double
# define MANT_DIG DBL_MANT_DIG
# define MIN DBL_MIN
# define L_(literal) literal
#else /* defined USE_FLOAT */
# define RINT rintf
# define DOUBLE float
# define MANT_DIG FLT_MANT_DIG
# define MIN FLT_MIN
# define L_(literal) literal##f
#endif
/* -0.0. See minus-zero.h. */
#if defined __hpux || defined __sgi || defined __ICC
# define MINUS_ZERO (-MIN * MIN)
#else
# define MINUS_ZERO L_(-0.0)
#endif
/* MSVC with option -fp:strict refuses to compile constant initializers that
contain floating-point operations. Pacify this compiler. */
#ifdef _MSC_VER
# pragma fenv_access (off)
#endif
DOUBLE
RINT (DOUBLE x)
{
/* 2^(MANT_DIG-1). */
static const DOUBLE TWO_MANT_DIG =
/* Assume MANT_DIG <= 5 * 31.
Use the identity
n = floor(n/5) + floor((n+1)/5) + ... + floor((n+4)/5). */
(DOUBLE) (1U << ((MANT_DIG - 1) / 5))
* (DOUBLE) (1U << ((MANT_DIG - 1 + 1) / 5))
* (DOUBLE) (1U << ((MANT_DIG - 1 + 2) / 5))
* (DOUBLE) (1U << ((MANT_DIG - 1 + 3) / 5))
* (DOUBLE) (1U << ((MANT_DIG - 1 + 4) / 5));
/* The use of 'volatile' guarantees that excess precision bits are dropped at
each addition step and before the following comparison at the caller's
site. It is necessary on x86 systems where double-floats are not IEEE
compliant by default, to avoid that the results become platform and
compiler option dependent. 'volatile' is a portable alternative to gcc's
-ffloat-store option. */
volatile DOUBLE z = x;
/* Consider the current rounding mode, cf.
<https://pubs.opengroup.org/onlinepubs/9699919799/basedefs/float.h.html>.
This implementation supports only rounds-to-nearest. */
if (FLT_ROUNDS != 1)
abort ();
if (z > L_(0.0))
{
/* Avoid rounding error for x = 0.5 - 2^(-MANT_DIG-1). */
if (z < L_(0.5))
z = L_(0.0);
/* Avoid rounding errors for values near 2^k, where k >= MANT_DIG-1. */
else if (z < TWO_MANT_DIG)
{
/* Round to the next integer. */
z += TWO_MANT_DIG;
z -= TWO_MANT_DIG;
}
}
else if (z < L_(0.0))
{
/* Avoid rounding error for x = -(0.5 - 2^(-MANT_DIG-1)). */
if (z > - L_(0.5))
z = MINUS_ZERO;
/* Avoid rounding errors for values near -2^k, where k >= MANT_DIG-1. */
else if (z > -TWO_MANT_DIG)
{
/* Round to the next integer. */
z -= TWO_MANT_DIG;
z += TWO_MANT_DIG;
}
}
return z;
}
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