// -*- C++ -*-
//===--------------------------- numeric ----------------------------------===//
//
//                     The LLVM Compiler Infrastructure
//
// This file is dual licensed under the MIT and the University of Illinois Open
// Source Licenses. See LICENSE.TXT for details.
//
//===----------------------------------------------------------------------===//

#ifndef _LIBCPP_EXPERIMENTAL_NUMERIC
#define _LIBCPP_EXPERIMENTAL_NUMERIC
/*
    experimental/numeric synopsis

// C++1z
namespace std {
namespace experimental {
inline namespace fundamentals_v2 {

  // 13.1.2, Greatest common divisor
  template<class M, class N>
  constexpr common_type_t<M,N> gcd(M m, N n);

  // 13.1.3, Least common multiple
  template<class M, class N>
  constexpr common_type_t<M,N> lcm(M m, N n);

} // namespace fundamentals_v2
} // namespace experimental
} // namespace std

 */

#include <experimental/__config>
#include <numeric>
#include <type_traits>              // is_integral
#include <limits>                   // numeric_limits

#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
#pragma GCC system_header
#endif

#if _LIBCPP_STD_VER > 11

_LIBCPP_BEGIN_NAMESPACE_LFTS_V2

template <typename _Result, typename _Source, bool _IsSigned = is_signed<_Source>::value> struct __abs;

template <typename _Result, typename _Source>
struct __abs<_Result, _Source, true> {
    _LIBCPP_CONSTEXPR _LIBCPP_INLINE_VISIBILITY
    _Result operator()(_Source __t) const noexcept
    {
    if (__t >= 0) return __t;
    if (__t == numeric_limits<_Source>::min()) return -static_cast<_Result>(__t);
    return -__t;
    }
};

template <typename _Result, typename _Source>
struct __abs<_Result, _Source, false> {
    _LIBCPP_CONSTEXPR _LIBCPP_INLINE_VISIBILITY
    _Result operator()(_Source __t) const noexcept { return __t; }
};


template<class _Tp>
_LIBCPP_CONSTEXPR _LIBCPP_INLINE_VISIBILITY
_Tp __gcd(_Tp __m, _Tp __n)
{
    static_assert((!is_signed<_Tp>::value), "" );
    return __n == 0 ? __m : __gcd<_Tp>(__n, __m % __n);
}


template<class _Tp, class _Up>
_LIBCPP_CONSTEXPR _LIBCPP_INLINE_VISIBILITY
common_type_t<_Tp,_Up>
gcd(_Tp __m, _Up __n)
{
    static_assert((is_integral<_Tp>::value && is_integral<_Up>::value), "Arguments to gcd must be integer types");
    static_assert((!is_same<typename remove_cv<_Tp>::type, bool>::value), "First argument to gcd cannot be bool" );
    static_assert((!is_same<typename remove_cv<_Up>::type, bool>::value), "Second argument to gcd cannot be bool" );
    using _Rp = common_type_t<_Tp,_Up>;
    using _Wp = make_unsigned_t<_Rp>;
    return static_cast<_Rp>(__gcd(static_cast<_Wp>(__abs<_Rp, _Tp>()(__m)),
                                  static_cast<_Wp>(__abs<_Rp, _Up>()(__n))));
}

template<class _Tp, class _Up>
_LIBCPP_CONSTEXPR _LIBCPP_INLINE_VISIBILITY
common_type_t<_Tp,_Up>
lcm(_Tp __m, _Up __n)
{
    static_assert((is_integral<_Tp>::value && is_integral<_Up>::value), "Arguments to lcm must be integer types");
    static_assert((!is_same<typename remove_cv<_Tp>::type, bool>::value), "First argument to lcm cannot be bool" );
    static_assert((!is_same<typename remove_cv<_Up>::type, bool>::value), "Second argument to lcm cannot be bool" );
    if (__m == 0 || __n == 0)
        return 0;

    using _Rp = common_type_t<_Tp,_Up>;
    _Rp __val1 = __abs<_Rp, _Tp>()(__m) / gcd(__m, __n);
    _Rp __val2 = __abs<_Rp, _Up>()(__n);
    _LIBCPP_ASSERT((numeric_limits<_Rp>::max() / __val1 > __val2), "Overflow in lcm");
    return __val1 * __val2;
}

_LIBCPP_END_NAMESPACE_LFTS_V2

#endif /* _LIBCPP_STD_VER > 11 */
#endif /* _LIBCPP_EXPERIMENTAL_NUMERIC */