lib/floor.c

   1 /* Round towards negative infinity.
   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 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 #ifdef USE_LONG_DOUBLE
  29 # define FUNC floorl
  30 # define DOUBLE long double
  31 # define MANT_DIG LDBL_MANT_DIG
  32 # define L_(literal) literal##L
  33 #elif ! defined USE_FLOAT
  34 # define FUNC floor
  35 # define DOUBLE double
  36 # define MANT_DIG DBL_MANT_DIG
  37 # define L_(literal) literal
  38 #else /* defined USE_FLOAT */
  39 # define FUNC floorf
  40 # define DOUBLE float
  41 # define MANT_DIG FLT_MANT_DIG
  42 # define L_(literal) literal##f
  43 #endif
  44
  45 /* MSVC with option -fp:strict refuses to compile constant initializers that
  46    contain floating-point operations.  Pacify this compiler.  */
  47 #if defined _MSC_VER && !defined __clang__
  48 # pragma fenv_access (off)
  49 #endif
  50
  51 /* 2^(MANT_DIG-1).  */
  52 static const DOUBLE TWO_MANT_DIG =
  53   /* Assume MANT_DIG <= 5 * 31.
  54      Use the identity
  55        n = floor(n/5) + floor((n+1)/5) + ... + floor((n+4)/5).  */
  56   (DOUBLE) (1U << ((MANT_DIG - 1) / 5))
  57   * (DOUBLE) (1U << ((MANT_DIG - 1 + 1) / 5))
  58   * (DOUBLE) (1U << ((MANT_DIG - 1 + 2) / 5))
  59   * (DOUBLE) (1U << ((MANT_DIG - 1 + 3) / 5))
  60   * (DOUBLE) (1U << ((MANT_DIG - 1 + 4) / 5));
  61
  62 DOUBLE
  63 FUNC (DOUBLE x)
  64 {
  65   /* The use of 'volatile' guarantees that excess precision bits are dropped
  66      at each addition step and before the following comparison at the caller's
  67      site.  It is necessary on x86 systems where double-floats are not IEEE
  68      compliant by default, to avoid that the results become platform and compiler
  69      option dependent.  'volatile' is a portable alternative to gcc's
  70      -ffloat-store option.  */
  71   volatile DOUBLE y = x;
  72   volatile DOUBLE z = y;
  73
  74   if (z > L_(0.0))
  75     {
  76       /* For 0 < x < 1, return +0.0 even if the current rounding mode is
  77          FE_DOWNWARD.  */
  78       if (z < L_(1.0))
  79         z = L_(0.0);
  80       /* Avoid rounding errors for values near 2^k, where k >= MANT_DIG-1.  */
  81       else if (z < TWO_MANT_DIG)
  82         {
  83           /* Round to the next integer (nearest or up or down, doesn't matter).  */
  84           z += TWO_MANT_DIG;
  85           z -= TWO_MANT_DIG;
  86           /* Enforce rounding down.  */
  87           if (z > y)
  88             z -= L_(1.0);
  89         }
  90     }
  91   else if (z < L_(0.0))
  92     {
  93       /* Avoid rounding errors for values near -2^k, where k >= MANT_DIG-1.  */
  94       if (z > - TWO_MANT_DIG)
  95         {
  96           /* Round to the next integer (nearest or up or down, doesn't matter).  */
  97           z -= TWO_MANT_DIG;
  98           z += TWO_MANT_DIG;
  99           /* Enforce rounding down.  */
 100           if (z > y)
 101             z -= L_(1.0);
 102         }
 103     }
 104   return z;
 105 }