$\left\lfloor \frac{x}{y} \right\rfloor$ (tools/floor.hpp)

template <typename M, typename N>
constexpr std::common_type_t<M, N> floor(M x, N y) noexcept;

It returns $\left\lfloor \frac{x}{y} \right\rfloor$.

Constraints

<M> is a built-in integral type, tools::int128_t or tools::uint128_t.
<N> is a built-in integral type, tools::int128_t or tools::uint128_t.
$y \neq 0$
$\lfloor \frac{x}{y} \rfloor$ is representable in type std::common_type_t<M, N>.

Time Complexity

$O(1)$

License

Author

anqooqie

Depends on

std::is_integral extended for tools::int128_t and tools::uint128_t (tools/is_integral.hpp)

Required by

Verified with

Code

#ifndef TOOLS_FLOOR_HPP
#define TOOLS_FLOOR_HPP

#include <cassert>
#include <type_traits>
#include "tools/is_integral.hpp"

namespace tools {

  template <typename M, typename N> requires (
    ::tools::is_integral_v<M> && !::std::is_same_v<::std::remove_cv_t<M>, bool> &&
    ::tools::is_integral_v<N> && !::std::is_same_v<::std::remove_cv_t<N>, bool>)
  constexpr ::std::common_type_t<M, N> floor(const M x, const N y) noexcept {
    assert(y != 0);
    if (y >= 0) {
      if (x >= 0) {
        return x / y;
      } else {
        return (x + 1) / y - 1;
      }
    } else {
      if (x > 0) {
        return (x - 1) / y - 1;
      } else {
        return x / y;
      }
    }
  }
}

#endif

#line 1 "tools/floor.hpp"



#include <cassert>
#include <type_traits>
#line 1 "tools/is_integral.hpp"



#line 5 "tools/is_integral.hpp"

namespace tools {
  template <typename T>
  struct is_integral : ::std::is_integral<T> {};

  template <typename T>
  inline constexpr bool is_integral_v = ::tools::is_integral<T>::value;
}


#line 7 "tools/floor.hpp"

namespace tools {

  template <typename M, typename N> requires (
    ::tools::is_integral_v<M> && !::std::is_same_v<::std::remove_cv_t<M>, bool> &&
    ::tools::is_integral_v<N> && !::std::is_same_v<::std::remove_cv_t<N>, bool>)
  constexpr ::std::common_type_t<M, N> floor(const M x, const N y) noexcept {
    assert(y != 0);
    if (y >= 0) {
      if (x >= 0) {
        return x / y;
      } else {
        return (x + 1) / y - 1;
      }
    } else {
      if (x > 0) {
        return (x - 1) / y - 1;
      } else {
        return x / y;
      }
    }
  }
}