1  /* Round towards zero.
       2     Copyright (C) 2007, 2010-2022 Free Software Foundation, Inc.
       3  
       4     This file is free software: you can redistribute it and/or modify
       5     it under the terms of the GNU Lesser General Public License as
       6     published by the Free Software Foundation, either version 3 of the
       7     License, or (at your option) any later version.
       8  
       9     This file 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 Lesser General Public License for more details.
      13  
      14     You should have received a copy of the GNU Lesser 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 truncl
      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 trunc
      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 truncf
      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  #if defined _MSC_VER && !defined __clang__
      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        /* For 0 < x < 1, return +0.0 even if the current rounding mode is
      89           FE_DOWNWARD.  */
      90        if (z < L_(1.0))
      91          z = L_(0.0);
      92        /* Avoid rounding errors for values near 2^k, where k >= MANT_DIG-1.  */
      93        else if (z < TWO_MANT_DIG)
      94          {
      95            /* Round to the next integer (nearest or up or down, doesn't matter).  */
      96            z += TWO_MANT_DIG;
      97            z -= TWO_MANT_DIG;
      98            /* Enforce rounding down.  */
      99            if (z > y)
     100              z -= L_(1.0);
     101          }
     102      }
     103    else if (z < L_(0.0))
     104      {
     105        /* For -1 < x < 0, return -0.0 regardless of the current rounding
     106           mode.  */
     107        if (z > L_(-1.0))
     108          z = MINUS_ZERO;
     109        /* Avoid rounding errors for values near -2^k, where k >= MANT_DIG-1.  */
     110        else if (z > - TWO_MANT_DIG)
     111          {
     112            /* Round to the next integer (nearest or up or down, doesn't matter).  */
     113            z -= TWO_MANT_DIG;
     114            z += TWO_MANT_DIG;
     115            /* Enforce rounding up.  */
     116            if (z < y)
     117              z += L_(1.0);
     118          }
     119      }
     120    return z;
     121  }