std::numeric_limits<T>::is_modulo

 

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static const bool is_modulo;		(until C++11)
static constexpr bool is_modulo;		(since C++11)

The value of std::numeric_limits<T>::is_modulo is true for all arithmetic types T that are possible to (until C++11)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.

(since C++11)

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T	value of std::numeric_limits<T>::is_modulo
/* non-specialized */	false
bool	false
char	implementation-defined
signed char	implementation-defined
unsigned char	true
wchar_t	implementation-defined
char8_t (C++20)	true
char16_t (C++11)	true
char32_t (C++11)	true
short	implementation-defined
unsigned short	true
int	implementation-defined
unsigned int	true
long	implementation-defined
unsigned long	true
long long (C++11)	implementation-defined
unsigned long long (C++11)	true
float	false
double	false
long double	false

Notes

Although the C++11 standard still says "On most machines, this is true for signed integers.", it is a defect and has been corrected. The exact wording changed from C++03 to C++11 in such a way that the true value is no longer compatible with undefined behavior on signed integer overflow. Because of that, the implementations that rely on signed overflow being undefined (for optimization opportunities) now set is_modulo to false for signed integers. See for example GCC PR 22200.

Example

Demonstrates the behavior of modulo types

Run this code

#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 << "\nmax 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>();
    check_overflow<unsigned long>();
    // check_overflow<float>(); // compile-time error, not a modulo type
}

Possible output:

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.

DR	Applied to	Behavior as published	Correct behavior
LWG 2422	C++11	is_modulo was required to true for signed integer types on most machines	required to be false for signed integer types unless signed integer overflow is defined to wrap

See also

is_integer [static]	identifies integer types (public static member constant)
is_iec559 [static]	identifies the IEC 559/IEEE 754 floating-point types (public static member constant)
is_exact [static]	identifies exact types (public static member constant)