lib/round.c

   1 /* Round toward nearest, breaking ties away from zero.
   2    Copyright (C) 2007, 2010-2020 Free Software Foundation, Inc.
   3
   4    This program is free software; you can redistribute it and/or modify
   5    it under the terms of the GNU General Public License as published by
   6    the Free Software Foundation; either version 2, or (at your option)
   7    any later version.
   8
   9    This program is distributed in the hope that it will be useful,
  10    but WITHOUT ANY WARRANTY; without even the implied warranty of
  11    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  12    GNU General Public License for more details.
  13
  14    You should have received a copy of the GNU General Public License along
  15    with this program; if not, see <https://www.gnu.org/licenses/>.  */
  16
  17 /* Written by Ben Pfaff <blp@gnu.org>, 2007.
  18    Based heavily on code by Bruno Haible. */
  19
  20 #if ! defined USE_LONG_DOUBLE
  21 # include <config.h>
  22 #endif
  23
  24 /* Specification.  */
  25 #include <math.h>
  26
  27 #include <float.h>
  28
  29 #undef MIN
  30
  31 #ifdef USE_LONG_DOUBLE
  32 # define ROUND roundl
  33 # define FLOOR floorl
  34 # define CEIL ceill
  35 # define DOUBLE long double
  36 # define MANT_DIG LDBL_MANT_DIG
  37 # define MIN LDBL_MIN
  38 # define L_(literal) literal##L
  39 # define HAVE_FLOOR_AND_CEIL HAVE_FLOORL_AND_CEILL
  40 #elif ! defined USE_FLOAT
  41 # define ROUND round
  42 # define FLOOR floor
  43 # define CEIL ceil
  44 # define DOUBLE double
  45 # define MANT_DIG DBL_MANT_DIG
  46 # define MIN DBL_MIN
  47 # define L_(literal) literal
  48 # define HAVE_FLOOR_AND_CEIL 1
  49 #else /* defined USE_FLOAT */
  50 # define ROUND roundf
  51 # define FLOOR floorf
  52 # define CEIL ceilf
  53 # define DOUBLE float
  54 # define MANT_DIG FLT_MANT_DIG
  55 # define MIN FLT_MIN
  56 # define L_(literal) literal##f
  57 # define HAVE_FLOOR_AND_CEIL HAVE_FLOORF_AND_CEILF
  58 #endif
  59
  60 /* -0.0.  See minus-zero.h.  */
  61 #if defined __hpux || defined __sgi || defined __ICC
  62 # define MINUS_ZERO (-MIN * MIN)
  63 #else
  64 # define MINUS_ZERO L_(-0.0)
  65 #endif
  66
  67 /* MSVC with option -fp:strict refuses to compile constant initializers that
  68    contain floating-point operations.  Pacify this compiler.  */
  69 #if defined _MSC_VER && !defined __clang__
  70 # pragma fenv_access (off)
  71 #endif
  72
  73 /* If we're being included from test-round2[f].c, it already defined names for
  74    our round implementations.  Otherwise, pick the preferred implementation for
  75    this machine. */
  76 #if !defined FLOOR_BASED_ROUND && !defined FLOOR_FREE_ROUND
  77 # if HAVE_FLOOR_AND_CEIL
  78 #  define FLOOR_BASED_ROUND ROUND
  79 # else
  80 #  define FLOOR_FREE_ROUND ROUND
  81 # endif
  82 #endif
  83
  84 #ifdef FLOOR_BASED_ROUND
  85 /* An implementation of the C99 round function based on floor and ceil.  We use
  86    this when floor and ceil are available, on the assumption that they are
  87    faster than the open-coded versions below. */
  88 DOUBLE
  89 FLOOR_BASED_ROUND (DOUBLE x)
  90 {
  91   if (x >= L_(0.0))
  92     {
  93       DOUBLE y = FLOOR (x);
  94       if (x - y >= L_(0.5))
  95         y += L_(1.0);
  96       return y;
  97     }
  98   else
  99     {
 100       DOUBLE y = CEIL (x);
 101       if (y - x >= L_(0.5))
 102         y -= L_(1.0);
 103       return y;
 104     }
 105 }
 106 #endif /* FLOOR_BASED_ROUND */
 107
 108 #ifdef FLOOR_FREE_ROUND
 109 /* An implementation of the C99 round function without floor or ceil.
 110    We use this when floor or ceil is missing. */
 111 DOUBLE
 112 FLOOR_FREE_ROUND (DOUBLE x)
 113 {
 114   /* 2^(MANT_DIG-1).  */
 115   static const DOUBLE TWO_MANT_DIG =
 116     /* Assume MANT_DIG <= 5 * 31.
 117        Use the identity
 118        n = floor(n/5) + floor((n+1)/5) + ... + floor((n+4)/5).  */
 119     (DOUBLE) (1U << ((MANT_DIG - 1) / 5))
 120     * (DOUBLE) (1U << ((MANT_DIG - 1 + 1) / 5))
 121     * (DOUBLE) (1U << ((MANT_DIG - 1 + 2) / 5))
 122     * (DOUBLE) (1U << ((MANT_DIG - 1 + 3) / 5))
 123     * (DOUBLE) (1U << ((MANT_DIG - 1 + 4) / 5));
 124
 125   /* The use of 'volatile' guarantees that excess precision bits are dropped at
 126      each addition step and before the following comparison at the caller's
 127      site.  It is necessary on x86 systems where double-floats are not IEEE
 128      compliant by default, to avoid that the results become platform and
 129      compiler option dependent.  'volatile' is a portable alternative to gcc's
 130      -ffloat-store option.  */
 131   volatile DOUBLE y = x;
 132   volatile DOUBLE z = y;
 133
 134   if (z > L_(0.0))
 135     {
 136       /* Avoid rounding error for x = 0.5 - 2^(-MANT_DIG-1).  */
 137       if (z < L_(0.5))
 138         z = L_(0.0);
 139       /* Avoid rounding errors for values near 2^k, where k >= MANT_DIG-1.  */
 140       else if (z < TWO_MANT_DIG)
 141         {
 142           /* Add 0.5 to the absolute value.  */
 143           y = z += L_(0.5);
 144           /* Round to the next integer (nearest or up or down, doesn't
 145              matter).  */
 146           z += TWO_MANT_DIG;
 147           z -= TWO_MANT_DIG;
 148           /* Enforce rounding down.  */
 149           if (z > y)
 150             z -= L_(1.0);
 151         }
 152     }
 153   else if (z < L_(0.0))
 154     {
 155       /* Avoid rounding error for x = -(0.5 - 2^(-MANT_DIG-1)).  */
 156       if (z > - L_(0.5))
 157         z = MINUS_ZERO;
 158       /* Avoid rounding errors for values near -2^k, where k >= MANT_DIG-1.  */
 159       else if (z > -TWO_MANT_DIG)
 160         {
 161           /* Add 0.5 to the absolute value.  */
 162           y = z -= L_(0.5);
 163           /* Round to the next integer (nearest or up or down, doesn't
 164              matter).  */
 165           z -= TWO_MANT_DIG;
 166           z += TWO_MANT_DIG;
 167           /* Enforce rounding up.  */
 168           if (z < y)
 169             z += L_(1.0);
 170         }
 171     }
 172   return z;
 173 }
 174 #endif /* FLOOR_FREE_ROUND */