lib/rint.c

   1 /* Round according to the current rounding mode.
   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 #if ! defined USE_LONG_DOUBLE
  18 # include <config.h>
  19 #endif
  20
  21 /* Specification.  */
  22 #include <math.h>
  23
  24 #include <float.h>
  25 #include <stdlib.h>
  26
  27 #undef MIN
  28
  29 #ifdef USE_LONG_DOUBLE
  30 # define RINT rintl
  31 # define DOUBLE long double
  32 # define MANT_DIG LDBL_MANT_DIG
  33 # define MIN LDBL_MIN
  34 # define L_(literal) literal##L
  35 #elif ! defined USE_FLOAT
  36 # define RINT rint
  37 # define DOUBLE double
  38 # define MANT_DIG DBL_MANT_DIG
  39 # define MIN DBL_MIN
  40 # define L_(literal) literal
  41 #else /* defined USE_FLOAT */
  42 # define RINT rintf
  43 # define DOUBLE float
  44 # define MANT_DIG FLT_MANT_DIG
  45 # define MIN FLT_MIN
  46 # define L_(literal) literal##f
  47 #endif
  48
  49 /* -0.0.  See minus-zero.h.  */
  50 #if defined __hpux || defined __sgi || defined __ICC
  51 # define MINUS_ZERO (-MIN * MIN)
  52 #else
  53 # define MINUS_ZERO L_(-0.0)
  54 #endif
  55
  56 /* MSVC with option -fp:strict refuses to compile constant initializers that
  57    contain floating-point operations.  Pacify this compiler.  */
  58 #if defined _MSC_VER && !defined __clang__
  59 # pragma fenv_access (off)
  60 #endif
  61
  62 DOUBLE
  63 RINT (DOUBLE x)
  64 {
  65   /* 2^(MANT_DIG-1).  */
  66   static const DOUBLE TWO_MANT_DIG =
  67     /* Assume MANT_DIG <= 5 * 31.
  68        Use the identity
  69        n = floor(n/5) + floor((n+1)/5) + ... + floor((n+4)/5).  */
  70     (DOUBLE) (1U << ((MANT_DIG - 1) / 5))
  71     * (DOUBLE) (1U << ((MANT_DIG - 1 + 1) / 5))
  72     * (DOUBLE) (1U << ((MANT_DIG - 1 + 2) / 5))
  73     * (DOUBLE) (1U << ((MANT_DIG - 1 + 3) / 5))
  74     * (DOUBLE) (1U << ((MANT_DIG - 1 + 4) / 5));
  75
  76   /* The use of 'volatile' guarantees that excess precision bits are dropped at
  77      each addition step and before the following comparison at the caller's
  78      site.  It is necessary on x86 systems where double-floats are not IEEE
  79      compliant by default, to avoid that the results become platform and
  80      compiler option dependent.  'volatile' is a portable alternative to gcc's
  81      -ffloat-store option.  */
  82   volatile DOUBLE z = x;
  83
  84   /* Consider the current rounding mode, cf.
  85      <https://pubs.opengroup.org/onlinepubs/9699919799/basedefs/float.h.html>.
  86      This implementation supports only rounds-to-nearest.  */
  87   if (FLT_ROUNDS != 1)
  88     abort ();
  89
  90   if (z > L_(0.0))
  91     {
  92       /* Avoid rounding error for x = 0.5 - 2^(-MANT_DIG-1).  */
  93       if (z < L_(0.5))
  94         z = L_(0.0);
  95       /* Avoid rounding errors for values near 2^k, where k >= MANT_DIG-1.  */
  96       else if (z < TWO_MANT_DIG)
  97         {
  98           /* Round to the next integer.  */
  99           z += TWO_MANT_DIG;
 100           z -= TWO_MANT_DIG;
 101         }
 102     }
 103   else if (z < L_(0.0))
 104     {
 105       /* Avoid rounding error for x = -(0.5 - 2^(-MANT_DIG-1)).  */
 106       if (z > - L_(0.5))
 107         z = MINUS_ZERO;
 108       /* Avoid rounding errors for values near -2^k, where k >= MANT_DIG-1.  */
 109       else if (z > -TWO_MANT_DIG)
 110         {
 111           /* Round to the next integer.  */
 112           z -= TWO_MANT_DIG;
 113           z += TWO_MANT_DIG;
 114         }
 115     }
 116   return z;
 117 }