lib/floor.c

/* Round towards negative infinity.
   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/>.  */

/* Written by 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
# define FUNC floorl
# define DOUBLE long double
# define MANT_DIG LDBL_MANT_DIG
# define L_(literal) literal##L
#elif ! defined USE_FLOAT
# define FUNC floor
# define DOUBLE double
# define MANT_DIG DBL_MANT_DIG
# define L_(literal) literal
#else /* defined USE_FLOAT */
# define FUNC floorf
# define DOUBLE float
# define MANT_DIG FLT_MANT_DIG
# define L_(literal) literal##f
#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

/* 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));

DOUBLE
FUNC (DOUBLE x)
{
  /* 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 y = x;
  volatile DOUBLE z = y;

  if (z > L_(0.0))
    {
      /* For 0 < x < 1, return +0.0 even if the current rounding mode is
         FE_DOWNWARD.  */
      if (z < L_(1.0))
        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 (nearest or up or down, doesn't matter).  */
          z += TWO_MANT_DIG;
          z -= TWO_MANT_DIG;
          /* Enforce rounding down.  */
          if (z > y)
            z -= L_(1.0);
        }
    }
  else if (z < L_(0.0))
    {
      /* Avoid rounding errors for values near -2^k, where k >= MANT_DIG-1.  */
      if (z > - TWO_MANT_DIG)
        {
          /* Round to the next integer (nearest or up or down, doesn't matter).  */
          z -= TWO_MANT_DIG;
          z += TWO_MANT_DIG;
          /* Enforce rounding down.  */
          if (z > y)
            z -= L_(1.0);
        }
    }
  return z;
}