libga68/floor.c

/* Round towards negative infinity.
   Copyright (C) 2007, 2010-2026 Free Software Foundation, Inc.

   Adapted from gnulib 0cca364da074782231685f955da2f0ce67d8c155.

   GCC 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, or (at your option) any later version.

   GCC 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.

   Under Section 7 of GPL version 3, you are granted additional permissions
   described in the GCC Runtime Library Exception, version 3.1, as published by
   the Free Software Foundation.

   You should have received a copy of the GNU General Public License and a copy
   of the GCC Runtime Library Exception along with this program; see the files
   COPYING3 and COPYING.RUNTIME respectively.  If not, see
   <http://www.gnu.org/licenses/>.  */

/* Written by Bruno Haible <bruno@clisp.org>, 2007.  */
/* Modified for libga68 by Jose E. Marchesi <jemarch@gnu.org>, 2026.  */

#include <float.h>

#ifdef USE_LONG_DOUBLE
# define FUNC floorl
# define DOUBLE long double
# define MANT_DIG LDBL_MANT_DIG
# define TWO_MANT_DIG LDBL_TWO_MANT_DIG
# define L_(literal) literal##L
#elif ! defined USE_FLOAT
# define FUNC floor
# define DOUBLE double
# define MANT_DIG DBL_MANT_DIG
# define TWO_MANT_DIG DBL_TWO_MANT_DIG
# define L_(literal) literal
#else /* defined USE_FLOAT */
# define FUNC floorf
# define DOUBLE float
# define MANT_DIG FLT_MANT_DIG
# define TWO_MANT_DIG FLT_TWO_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;
}

#undef FUNC
#undef DOUBLE
#undef MANT_DIG
#undef TWO_MANT_DIG
#undef L_