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.

Standard specializations

Notes

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

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

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.

See also