std::div,std::ldiv,std::lldiv,std::imaxdiv(3)

NAME
std::div,std::ldiv,std::lldiv,std::imaxdiv - std::div,std::ldiv,std::lldiv,std::imaxdiv

Synopsis
   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> (since C++11)
   if and only if std::intmax_t is an extended integer type.
   The quotient is the algebraic quotient with any fractional part
   discarded (truncated towards zero). The remainder is such that quot * (until C++11)
   y + rem == x.
   The quotient is the result of the expression x / y. The remainder is (since C++11)
   the result of the expression x % y.

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

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

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