lib/rint.c

/* Round according to the current rounding mode.
   Copyright (C) 2007, 2010-2026 Free Software Foundation, Inc.

   This file 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.

   This file 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 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 __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.  */
#if defined _MSC_VER && !defined __clang__
# 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;
}