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# std::numeric_limits::is_modulo

From cppreference.com
< cpp‎ | types‎ | numeric limits

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 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.

### [edit] Standard specializations

`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
char16_t | implementation-defined
char32_t | implementation-defined
short | implementation-defined
unsigned short | true
int | implementation-defined
unsigned int | true
long | implementation-defined
unsigned long | true
long long | implementation-defined
unsigned long long | true
float | false
double | false
long double | false

### [edit] Notes

Although the C++11 standard still says "On most machines, this is true for signed integers.", 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 (it changed from "possible" to a strict requirement). 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.

The standard wording is expected to change to "is_modulo is false for signed integer types unless an implementation defines signed integer overflow to wrap" per LWG issue 2422.

### [edit] 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

### [edit] See also

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

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