# std::div, std::ldiv, std::lldiv, std::imaxdiv

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< cpp‎ | numeric‎ | math

Defined in header `<cstdlib>` |  |
std::div_t div( int x, int y ); | (1) | (constexpr since C++23)
std::ldiv_t div( long x, long y ); | (2) | (constexpr since C++23)
std::lldiv_t div( long long x, long long y ); | (3) | (since C++11) (constexpr since C++23)
std::ldiv_t ldiv( long x, long y ); | (4) | (constexpr since C++23)
std::lldiv_t lldiv( long long x, long long y ); | (5) | (since C++11) (constexpr since C++23)
Defined in header `<cinttypes>` |  |
std::imaxdiv_t div( std::intmax_t x, std::intmax_t y ); | (6) | (since C++11) (constexpr since C++23)
std::imaxdiv_t imaxdiv( std::intmax_t x, std::intmax_t y ); | (7) | (since C++11) (constexpr since C++23)

Computes both the quotient and the remainder of the division of the numerator x by the denominator y.

6-7) Overload of `std::div` for std::intmax_t is provided in `<cinttypes>` if and only if std::intmax_t is an extended integer type. | (since C++11)

The quotient is the algebraic quotient with any fractional part discarded (truncated towards zero). The remainder is such that quot * y + rem == x. | (until C++11)
The quotient is the result of the expression x / y. The remainder is the result of the expression x % y. | (since C++11)

### Parameters

x, y | - | integer values

### Return value

If both the remainder and the quotient can be represented as objects of the corresponding type (int, long, long long, std::intmax_t, respectively), returns both as an object of type `std::div_t`, `std::ldiv_t`, `std::lldiv_t`, `std::imaxdiv_t` defined as follows:

## std::div_t

    struct div_t { int quot; int rem; };

or

    struct div_t { int rem; int quot; };

## std::ldiv_t

    struct ldiv_t { long quot; long rem; };

or

    struct ldiv_t { long rem; long quot; };

## std::lldiv_t

    struct lldiv_t { long long quot; long long rem; };

or

    struct lldiv_t { long long rem; long long quot; };

## std::imaxdiv_t

    struct imaxdiv_t { std::intmax_t quot; std::intmax_t rem; };

or

    struct imaxdiv_t { std::intmax_t rem; std::intmax_t quot; };

If either the remainder or the quotient cannot be represented, the behavior is undefined.

### Notes

Until C++11, the rounding direction of the quotient and the sign of the remainder in the built-in division and remainder operators was implementation-defined if either of the operands was negative, but it was well-defined in `std::div`.

On many platforms, a single CPU instruction obtains both the quotient and the remainder, and this function may leverage that, although compilers are generally able to merge nearby `/` and `%` where suitable.

### Example

Run this code

    #include <cassert>
    #include <cmath>
    #include <cstdlib>
    #include <iostream>
    #include <sstream>
    #include <string>

    std::string euclidean_division_string(int dividend, int divisor)
    {
        auto dv = std::div(dividend, divisor);
        assert(dividend == divisor * dv.quot + dv.rem);
        assert(dv.quot == dividend / divisor);
        assert(dv.rem == dividend % divisor);

        auto sign = [](int n){ return n > 0 ? 1 : n < 0 ? -1 : 0; };
        assert((dv.rem == 0) or (sign(dv.rem) == sign(dividend)));

        return (std::ostringstream() << std::showpos << dividend << " = "
                                     << divisor << " * (" << dv.quot << ") "
                                     << std::showpos << dv.rem).str();
    }

    std::string itoa(int n, int radix /*[2..16]*/)
    {
        std::string buf;
        std::div_t dv{}; dv.quot = n;

        do
        {
            dv = std::div(dv.quot, radix);
            buf += "0123456789abcdef"[std::abs(dv.rem)]; // string literals are arrays
        }
        while(dv.quot);

        if (n < 0)
            buf += '-';

        return {buf.rbegin(), buf.rend()};
    }

    int main()
    {
        std::cout << euclidean_division_string(369, 10) << '\n'
                  << euclidean_division_string(369, -10) << '\n'
                  << euclidean_division_string(-369, 10) << '\n'
                  << euclidean_division_string(-369, -10) << "\n\n";

        std::cout << itoa(12345, 10) << '\n'
                  << itoa(-12345, 10) << '\n'
                  << itoa(42, 2) << '\n'
                  << itoa(65535, 16) << '\n';
    }

Output:

    +369 = +10 * (+36) +9
    +369 = -10 * (-36) +9
    -369 = +10 * (-36) -9
    -369 = -10 * (+36) -9

    12345
    -12345
    101010
    ffff

### See also

fmod fmodf fmodl (C++11)(C++11) | remainder of the floating point division operation (function)
remainder remainderf remainderl (C++11)(C++11)(C++11) | signed remainder of the division operation (function)
remquo remquof remquol (C++11)(C++11)(C++11) | signed remainder as well as the three last bits of the division operation (function)

### External links

Euclidean division

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