std::numeric_limits<T>::is_modulo

The value of std::numeric_limits<T>::is_modulo is true for all arithmetic types T that handle overflows with modulo arithmetic, that is, if the result of addition, subtraction, multiplication, or division of this type would fall outside the range [min(), max()], the value returned by such operation differs from the expected value by a multiple of max() - min() + 1.

is_modulo is false for signed integer types, unless the implementation defines signed integer overflow to wrap.

[edit] Standard specializations

[edit] Notes

The standard said "On most machines, this is true for signed integers." before the resolution of LWG issue 2422. See GCC PR 22200 for a related discussion.

[edit] Example

#include <iostream>
#include <type_traits>
#include <limits>
 
template<class T>
typename std::enable_if<std::numeric_limits<T>::is_modulo>::type
    check_overflow()
{
    std::cout << "max value is " << std::numeric_limits<T>::max() << '\n'
              << "min value is " << std::numeric_limits<T>::min() << '\n'
              << "max value + 1 is " << std::numeric_limits<T>::max()+1 << '\n';
}
 
int main()
{
    check_overflow<int>();
    std::cout << '\n';
    check_overflow<unsigned long>();
//  check_overflow<float>(); // compile-time error, not a modulo type
}

max value is 2147483647
min value is -2147483648
max value + 1 is -2147483648
 
max value is 18446744073709551615
min value is 0
max value + 1 is 0

[edit] Defect reports

The following behavior-changing defect reports were applied retroactively to previously published C++ standards.

1. ↑ The definition is "adding two positive numbers can have a result that wraps around to a third number that is less". It has the following problems:
   • It does not define the wrapped value.
   • It does not state whether result is repeatable.
   • It does not require that doing addition, subtraction and other operations on all values have defined behavior.

[edit] See also