lib/ceil.c

   1 /* Round towards positive infinity.
   2    Copyright (C) 2007, 2010-2018 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 3 of the License, or
   7    (at your option) 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
  15    along with this program.  If not, see <https://www.gnu.org/licenses/>.  */
  16
  17 /* Written by Bruno Haible <bruno@clisp.org>, 2007.  */
  18
  19 #if ! defined USE_LONG_DOUBLE
  20 # include <config.h>
  21 #endif
  22
  23 /* Specification.  */
  24 #include <math.h>
  25
  26 #include <float.h>
  27
  28 #undef MIN
  29
  30 #ifdef USE_LONG_DOUBLE
  31 # define FUNC ceill
  32 # define DOUBLE long double
  33 # define MANT_DIG LDBL_MANT_DIG
  34 # define MIN LDBL_MIN
  35 # define L_(literal) literal##L
  36 #elif ! defined USE_FLOAT
  37 # define FUNC ceil
  38 # define DOUBLE double
  39 # define MANT_DIG DBL_MANT_DIG
  40 # define MIN DBL_MIN
  41 # define L_(literal) literal
  42 #else /* defined USE_FLOAT */
  43 # define FUNC ceilf
  44 # define DOUBLE float
  45 # define MANT_DIG FLT_MANT_DIG
  46 # define MIN FLT_MIN
  47 # define L_(literal) literal##f
  48 #endif
  49
  50 /* -0.0.  See minus-zero.h.  */
  51 #if defined __hpux || defined __sgi || defined __ICC
  52 # define MINUS_ZERO (-MIN * MIN)
  53 #else
  54 # define MINUS_ZERO L_(-0.0)
  55 #endif
  56
  57 /* MSVC with option -fp:strict refuses to compile constant initializers that
  58    contain floating-point operations.  Pacify this compiler.  */
  59 #ifdef _MSC_VER
  60 # pragma fenv_access (off)
  61 #endif
  62
  63 /* 2^(MANT_DIG-1).  */
  64 static const DOUBLE TWO_MANT_DIG =
  65   /* Assume MANT_DIG <= 5 * 31.
  66      Use the identity
  67        n = floor(n/5) + floor((n+1)/5) + ... + floor((n+4)/5).  */
  68   (DOUBLE) (1U << ((MANT_DIG - 1) / 5))
  69   * (DOUBLE) (1U << ((MANT_DIG - 1 + 1) / 5))
  70   * (DOUBLE) (1U << ((MANT_DIG - 1 + 2) / 5))
  71   * (DOUBLE) (1U << ((MANT_DIG - 1 + 3) / 5))
  72   * (DOUBLE) (1U << ((MANT_DIG - 1 + 4) / 5));
  73
  74 DOUBLE
  75 FUNC (DOUBLE x)
  76 {
  77   /* The use of 'volatile' guarantees that excess precision bits are dropped
  78      at each addition step and before the following comparison at the caller's
  79      site.  It is necessary on x86 systems where double-floats are not IEEE
  80      compliant by default, to avoid that the results become platform and compiler
  81      option dependent.  'volatile' is a portable alternative to gcc's
  82      -ffloat-store option.  */
  83   volatile DOUBLE y = x;
  84   volatile DOUBLE z = y;
  85
  86   if (z > L_(0.0))
  87     {
  88       /* Avoid rounding errors for values near 2^k, where k >= MANT_DIG-1.  */
  89       if (z < TWO_MANT_DIG)
  90         {
  91           /* Round to the next integer (nearest or up or down, doesn't matter).  */
  92           z += TWO_MANT_DIG;
  93           z -= TWO_MANT_DIG;
  94           /* Enforce rounding up.  */
  95           if (z < y)
  96             z += L_(1.0);
  97         }
  98     }
  99   else if (z < L_(0.0))
 100     {
 101       /* For -1 < x < 0, return -0.0 regardless of the current rounding
 102          mode.  */
 103       if (z > L_(-1.0))
 104         z = MINUS_ZERO;
 105       /* Avoid rounding errors for values near -2^k, where k >= MANT_DIG-1.  */
 106       else if (z > - TWO_MANT_DIG)
 107         {
 108           /* Round to the next integer (nearest or up or down, doesn't matter).  */
 109           z -= TWO_MANT_DIG;
 110           z += TWO_MANT_DIG;
 111           /* Enforce rounding up.  */
 112           if (z < y)
 113             z += L_(1.0);
 114         }
 115     }
 116   return z;
 117 }