sat_arith.h

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// Saturation arithmetic -*- C++ -*-
 
// Copyright The GNU Toolchain Authors.
//
// This file is part of the GNU ISO C++ Library.  This library is free
// software; you can redistribute it and/or modify it under the
// terms of the GNU General Public License as published by the
// Free Software Foundation; either version 3, or (at your option)
// any later version.
 
// This library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.
 
// Under Section 7 of GPL version 3, you are granted additional
// permissions described in the GCC Runtime Library Exception, version
// 3.1, as published by the Free Software Foundation.
 
// You should have received a copy of the GNU General Public License and
// a copy of the GCC Runtime Library Exception along with this program;
// see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see
// <http://www.gnu.org/licenses/>.
 
/** @file include/bits/sat_arith.h
 *  This is an internal header file, included by other library headers.
 *  Do not attempt to use it directly. @headername{numeric}
 */
 
#ifndef _GLIBCXX_SAT_ARITH_H
#define _GLIBCXX_SAT_ARITH_H 1
 
#ifdef _GLIBCXX_SYSHDR
#pragma GCC system_header
#endif
 
#include <bits/version.h>
 
#ifdef __glibcxx_saturation_arithmetic // C++ >= 26
 
#include <concepts>
#include <ext/numeric_traits.h>
 
namespace std _GLIBCXX_VISIBILITY(default)
{
_GLIBCXX_BEGIN_NAMESPACE_VERSION
 
  /// Add two integers, with saturation in case of overflow.
  template<typename _Tp> requires __is_signed_or_unsigned_integer<_Tp>::value
    constexpr _Tp
    saturating_add(_Tp __x, _Tp __y) noexcept
    {
      _Tp __z;
      if (!__builtin_add_overflow(__x, __y, &__z))
        return __z;
      if constexpr (is_unsigned_v<_Tp>)
        return __gnu_cxx::__int_traits<_Tp>::__max;
      else if (__x < 0)
        return __gnu_cxx::__int_traits<_Tp>::__min;
      else
        return __gnu_cxx::__int_traits<_Tp>::__max;
    }
 
  /// Subtract one integer from another, with saturation in case of overflow.
  template<typename _Tp> requires __is_signed_or_unsigned_integer<_Tp>::value
    constexpr _Tp
    saturating_sub(_Tp __x, _Tp __y) noexcept
    {
      _Tp __z;
      if (!__builtin_sub_overflow(__x, __y, &__z))
        return __z;
      if constexpr (is_unsigned_v<_Tp>)
        return __gnu_cxx::__int_traits<_Tp>::__min;
      else if (__x < 0)
        return __gnu_cxx::__int_traits<_Tp>::__min;
      else
        return __gnu_cxx::__int_traits<_Tp>::__max;
    }
 
  /// Multiply two integers, with saturation in case of overflow.
  template<typename _Tp> requires __is_signed_or_unsigned_integer<_Tp>::value
    constexpr _Tp
    saturating_mul(_Tp __x, _Tp __y) noexcept
    {
      _Tp __z;
      if (!__builtin_mul_overflow(__x, __y, &__z))
        return __z;
      if constexpr (is_unsigned_v<_Tp>)
        return __gnu_cxx::__int_traits<_Tp>::__max;
      else if ((__x < 0) != (__y < 0))
        return __gnu_cxx::__int_traits<_Tp>::__min;
      else
        return __gnu_cxx::__int_traits<_Tp>::__max;
    }
 
  /// Divide one integer by another, with saturation in case of overflow.
  template<typename _Tp> requires __is_signed_or_unsigned_integer<_Tp>::value
    constexpr _Tp
    saturating_div(_Tp __x, _Tp __y) noexcept
    {
      __glibcxx_assert(__y != 0);
      if constexpr (is_signed_v<_Tp>)
        if (__x == __gnu_cxx::__int_traits<_Tp>::__min && __y == _Tp(-1))
          return __gnu_cxx::__int_traits<_Tp>::__max;
      return __x / __y;
    }
 
  /// Divide one integer by another, with saturation in case of overflow.
  template<typename _Res, typename _Tp>
    requires __is_signed_or_unsigned_integer<_Res>::value
      && __is_signed_or_unsigned_integer<_Tp>::value
    constexpr _Res
    saturating_cast(_Tp __x) noexcept
    {
      constexpr int __digits_R = __gnu_cxx::__int_traits<_Res>::__digits;
      constexpr int __digits_T = __gnu_cxx::__int_traits<_Tp>::__digits;
      constexpr _Res __max_Res = __gnu_cxx::__int_traits<_Res>::__max;
 
      if constexpr (is_signed_v<_Res> == is_signed_v<_Tp>)
        {
          if constexpr (__digits_R < __digits_T)
            {
              constexpr _Res __min_Res = __gnu_cxx::__int_traits<_Res>::__min;
 
              if (__x < static_cast<_Tp>(__min_Res))
                return __min_Res;
              else if (__x > static_cast<_Tp>(__max_Res))
                return __max_Res;
            }
        }
      else if constexpr (is_signed_v<_Tp>) // Res is unsigned
        {
          if (__x < 0)
            return 0;
          else if (make_unsigned_t<_Tp>(__x) > __max_Res)
            return __gnu_cxx::__int_traits<_Res>::__max;
        }
      else // Tp is unsigned, Res is signed
        {
          if (__x > make_unsigned_t<_Res>(__max_Res))
            return __max_Res;
        }
      return static_cast<_Res>(__x);
    }
 
_GLIBCXX_END_NAMESPACE_VERSION
} // namespace
 
#endif // __glibcxx_saturation_arithmetic
#endif /* _GLIBCXX_SAT_ARITH_H */