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-/* Round toward nearest, breaking ties away from zero.
- Copyright (C) 2007, 2010-2011 Free Software Foundation, Inc.
-
- This program 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 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 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, write to the Free Software Foundation,
- Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA. */
-
-/* Written by Ben Pfaff <blp@gnu.org>, 2007.
- Based heavily on code by Bruno Haible. */
-
-#include <config.h>
-
-/* Specification. */
-#include <math.h>
-
-#include <float.h>
-
-#undef MIN
-
-#ifdef USE_LONG_DOUBLE
-# define ROUND roundl
-# define FLOOR floorl
-# define CEIL ceill
-# define DOUBLE long double
-# define MANT_DIG LDBL_MANT_DIG
-# define MIN LDBL_MIN
-# define L_(literal) literal##L
-# define HAVE_FLOOR_AND_CEIL HAVE_FLOORL_AND_CEILL
-#elif ! defined USE_FLOAT
-# define ROUND round
-# define FLOOR floor
-# define CEIL ceil
-# define DOUBLE double
-# define MANT_DIG DBL_MANT_DIG
-# define MIN DBL_MIN
-# define L_(literal) literal
-# define HAVE_FLOOR_AND_CEIL 1
-#else /* defined USE_FLOAT */
-# define ROUND roundf
-# define FLOOR floorf
-# define CEIL ceilf
-# define DOUBLE float
-# define MANT_DIG FLT_MANT_DIG
-# define MIN FLT_MIN
-# define L_(literal) literal##f
-# define HAVE_FLOOR_AND_CEIL HAVE_FLOORF_AND_CEILF
-#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
-
-/* If we're being included from test-round2[f].c, it already defined names for
- our round implementations. Otherwise, pick the preferred implementation for
- this machine. */
-#if !defined FLOOR_BASED_ROUND && !defined FLOOR_FREE_ROUND
-# if HAVE_FLOOR_AND_CEIL
-# define FLOOR_BASED_ROUND ROUND
-# else
-# define FLOOR_FREE_ROUND ROUND
-# endif
-#endif
-
-#ifdef FLOOR_BASED_ROUND
-/* An implementation of the C99 round function based on floor and ceil. We use
- this when floor and ceil are available, on the assumption that they are
- faster than the open-coded versions below. */
-DOUBLE
-FLOOR_BASED_ROUND (DOUBLE x)
-{
- if (x >= L_(0.0))
- {
- DOUBLE y = FLOOR (x);
- if (x - y >= L_(0.5))
- y += L_(1.0);
- return y;
- }
- else
- {
- DOUBLE y = CEIL (x);
- if (y - x >= L_(0.5))
- y -= L_(1.0);
- return y;
- }
-}
-#endif /* FLOOR_BASED_ROUND */
-
-#ifdef FLOOR_FREE_ROUND
-/* An implementation of the C99 round function without floor or ceil.
- We use this when floor or ceil is missing. */
-DOUBLE
-FLOOR_FREE_ROUND (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 y = x;
- volatile DOUBLE z = y;
-
- 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)
- {
- /* Add 0.5 to the absolute value. */
- y = z += L_(0.5);
- /* 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 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)
- {
- /* Add 0.5 to the absolute value. */
- y = z -= L_(0.5);
- /* Round to the next integer (nearest or up or down, doesn't
- matter). */
- z -= TWO_MANT_DIG;
- z += TWO_MANT_DIG;
- /* Enforce rounding up. */
- if (z < y)
- z += L_(1.0);
- }
- }
- return z;
-}
-#endif /* FLOOR_FREE_ROUND */
-