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

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 CWG issue 614 was resolved (N2757), 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 division_with_remainder_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 << division_with_remainder_string(369, 10) << '\n'
              << division_with_remainder_string(369, -10) << '\n'
              << division_with_remainder_string(-369, 10) << '\n'
              << division_with_remainder_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

External links

1.	Euclidean division — From Wikipedia.
2.	Modulo (and Truncated division) — From Wikipedia.

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External libraries

fmodfmodffmodl (C++11)(C++11)	remainder of the floating point division operation (function)
remainderremainderfremainderl (C++11)(C++11)(C++11)	signed remainder of the division operation (function)
remquoremquofremquol (C++11)(C++11)(C++11)	signed remainder as well as the three last bits of the division operation (function)
C documentation for div