// -*- C++ -*-
//===----------------------------------------------------------------------===//
//
// Part of libcu++, the C++ Standard Library for your entire system,
// under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
// SPDX-FileCopyrightText: Copyright (c) 2024 NVIDIA CORPORATION & AFFILIATES.
//
//===----------------------------------------------------------------------===//

#ifndef _LIBCUDACXX___NUMERIC_GCD_LCM_H
#define _LIBCUDACXX___NUMERIC_GCD_LCM_H

#include <cuda/std/detail/__config>

#if defined(_CCCL_IMPLICIT_SYSTEM_HEADER_GCC)
#  pragma GCC system_header
#elif defined(_CCCL_IMPLICIT_SYSTEM_HEADER_CLANG)
#  pragma clang system_header
#elif defined(_CCCL_IMPLICIT_SYSTEM_HEADER_MSVC)
#  pragma system_header
#endif // no system header

#include <cuda/std/__type_traits/common_type.h>
#include <cuda/std/__type_traits/is_integral.h>
#include <cuda/std/__type_traits/is_same.h>
#include <cuda/std/__type_traits/is_signed.h>
#include <cuda/std/__type_traits/make_unsigned.h>
#include <cuda/std/limits>

_CCCL_PUSH_MACROS

_LIBCUDACXX_BEGIN_NAMESPACE_STD

template <typename _Result, typename _Source, bool _IsSigned = _CCCL_TRAIT(is_signed, _Source)>
struct __ct_abs;

template <typename _Result, typename _Source>
struct __ct_abs<_Result, _Source, true>
{
  constexpr _LIBCUDACXX_HIDE_FROM_ABI _Result operator()(_Source __t) const noexcept
  {
    if (__t >= 0)
    {
      return __t;
    }
    _CCCL_DIAG_PUSH
    _CCCL_DIAG_SUPPRESS_MSVC(4146) // unary minus operator applied to unsigned type, result still unsigned
    if (__t == (numeric_limits<_Source>::min)())
    {
      return -static_cast<_Result>(__t);
    }
    _CCCL_DIAG_POP
    return -__t;
  }
};

template <typename _Result, typename _Source>
struct __ct_abs<_Result, _Source, false>
{
  constexpr _LIBCUDACXX_HIDE_FROM_ABI _Result operator()(_Source __t) const noexcept
  {
    return __t;
  }
};

template <class _Tp>
constexpr _LIBCUDACXX_HIDE_FROM_ABI _Tp __gcd(_Tp __m, _Tp __n)
{
  static_assert((!_CCCL_TRAIT(is_signed, _Tp)), "");
  return __n == 0 ? __m : _CUDA_VSTD::__gcd<_Tp>(__n, __m % __n);
}

template <class _Tp, class _Up>
constexpr _LIBCUDACXX_HIDE_FROM_ABI common_type_t<_Tp, _Up> gcd(_Tp __m, _Up __n)
{
  static_assert((_CCCL_TRAIT(is_integral, _Tp) && _CCCL_TRAIT(is_integral, _Up)),
                "Arguments to gcd must be integer types");
  static_assert((!_CCCL_TRAIT(is_same, remove_cv_t<_Tp>, bool)), "First argument to gcd cannot be bool");
  static_assert((!_CCCL_TRAIT(is_same, remove_cv_t<_Up>, bool)), "Second argument to gcd cannot be bool");
  using _Rp = common_type_t<_Tp, _Up>;
  using _Wp = make_unsigned_t<_Rp>;
  return static_cast<_Rp>(
    _CUDA_VSTD::__gcd(static_cast<_Wp>(__ct_abs<_Rp, _Tp>()(__m)), static_cast<_Wp>(__ct_abs<_Rp, _Up>()(__n))));
}

template <class _Tp, class _Up>
constexpr _LIBCUDACXX_HIDE_FROM_ABI common_type_t<_Tp, _Up> lcm(_Tp __m, _Up __n)
{
  static_assert((_CCCL_TRAIT(is_integral, _Tp) && _CCCL_TRAIT(is_integral, _Up)),
                "Arguments to lcm must be integer types");
  static_assert((!_CCCL_TRAIT(is_same, remove_cv_t<_Tp>, bool)), "First argument to lcm cannot be bool");
  static_assert((!_CCCL_TRAIT(is_same, remove_cv_t<_Up>, bool)), "Second argument to lcm cannot be bool");
  if (__m == 0 || __n == 0)
  {
    return 0;
  }

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

_LIBCUDACXX_END_NAMESPACE_STD

_CCCL_POP_MACROS

#endif // _LIBCUDACXX___NUMERIC_GCD_LCM_H
