bounded_arithmetic.h

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///  @file
 
#ifndef MYSQL_MATH_BOUNDED_ARITHMETIC_H
#define MYSQL_MATH_BOUNDED_ARITHMETIC_H
 
#include <type_traits>  // std::enable_if
 
/// @addtogroup GroupLibsMysqlMath
/// @{
 
namespace mysql::math {
 
/// Return x+y, limited to the given maximum.
///
/// @note This works even when x+y would exceed the maximum for the
/// datatype.
///
/// @tparam T Data type. Must be an unsigned integral datatype.
///
/// @param x The first term.
///
/// @param y The second term.
///
/// @param maximum The maximum allowed value.
///
/// @return The smallest of (x + y) and (maximum), computed as if
/// using infinite precision arithmetic.
template <typename T, std::enable_if_t<std::is_integral<T>::value &&
                                           std::is_unsigned<T>::value,
                                       bool> = true>
constexpr T add_bounded(const T x, const T y, const T maximum) {
  if (y >= maximum || maximum - y < x) return maximum;
  return x + y;
}
 
/// Return x*y, limited to the given maximum.
///
/// @note This works even when x * y would exceed the maximum for any of the
/// data type.
///
/// @tparam T Data type for the first factor, the maximum, and the
/// result.  This must be an unsigned integral.
///
/// @tparam T2 datatype for the second factor.  This can be any
/// arithmetic type, including floating point types.
///
/// @param x The first factor.
///
/// @param y The second factor.
///
/// @param maximum The maximum allowed value.
///
/// @return The smallest of (x + y) and (maximum), computed as if
/// using infinite precision arithmetic; or 0 if y is negative.
template <
    typename T, typename T2,
    std::enable_if_t<std::is_integral<T>::value && std::is_unsigned<T>::value &&
                         std::is_arithmetic<T2>::value,
                     bool> = true>
constexpr T multiply_bounded(const T x, const T2 y, const T maximum) {
  if (y <= 0) return 0;
  if (y > 1 && static_cast<T>(maximum / y) < x) return maximum;
  return static_cast<T>(x * y);
}
 
/// Return ceil(x / y), where x and y are unsigned integer types
template <typename T, std::enable_if_t<std::is_integral<T>::value &&
                                           std::is_unsigned<T>::value,
                                       bool> = true>
constexpr T ceil_div(const T x, const T y) {
  return (x + y - 1) / y;
}
 
}  // namespace mysql::math
 
/// @}
 
#endif  // MYSQL_MATH_BOUNDED_ARITHMETIC_H