#if !defined(TORCH_STABLE_ONLY) && !defined(TORCH_TARGET_VERSION)
#pragma once
// Please note that this file is
// used across both CPU and GPU.

#include <type_traits>
#include <complex>
#include <c10/macros/Macros.h>
#include <ATen/detail/FunctionTraits.h>
#include <ATen/NumericUtils.h>
#include <ATen/OpMathType.h>
#if defined(__CUDACC__)
#include <ATen/cuda/DeviceUtils.cuh>
#include <ATen/native/cuda/DeviceSqrt.cuh>
#elif defined(__HIPCC__)
#include <ATen/hip/DeviceUtils.cuh>
#include <ATen/native/hip/DeviceSqrt.cuh>
#endif
#if defined(__CUDACC__) || defined(__HIPCC__)
#include <thrust/pair.h>
#else
#include <cmath>
#define device_sqrt std::sqrt
#endif
#if defined(__CUDACC__) || defined(__HIPCC__)
template <typename scalar_t>
inline C10_DEVICE scalar_t max_propagate_nan(scalar_t a, scalar_t b) {
#if defined(__HIPCC__)
  // TODO: remove this special case for HIP when issue is fixed:
  //       https://github.com/ROCm/hip/issues/2209
  scalar_t max = at::_isnan(a) ? a : (at::_isnan(b) ? b : std::max(a, b));
#else
  scalar_t max = at::_isnan(b) ? b : std::max(a, b);
#endif
  return max;
}
template <typename scalar_t>
inline C10_DEVICE scalar_t min_propagate_nan(scalar_t a, scalar_t b) {
#if defined(__HIPCC__)
  // TODO: remove this special case for HIP when issue is fixed:
  //       https://github.com/ROCm/hip/issues/2209
  scalar_t min = at::_isnan(a) ? a : (at::_isnan(b) ? b : std::min(a, b));
#else
  scalar_t min = at::_isnan(b) ? b : std::min(a, b);
#endif
  return min;
}
#define MAX(X, Y) max_propagate_nan(X,Y)
#define MIN(X, Y) min_propagate_nan(X,Y)
#else
#include <ATen/native/cpu/zmath.h>
#define MAX(X, Y) max_impl(X,Y)
#define MIN(X, Y) min_impl(X,Y)
#endif

// ROCM hcc doesn't work well with using std:: in kernel functions
#if defined(__CUDA_ARCH__)
#include <c10/cuda/CUDAMathCompat.h>
#define compat_pow c10::cuda::compat::pow
#elif defined(__HIPCC__)
#include <c10/hip/HIPMathCompat.h>
#define compat_pow c10::hip::compat::pow
#else
#define compat_pow std::pow
#endif

namespace at::native {

namespace detail {

#if defined(__CUDACC__) || defined(__HIPCC__)
template <typename T1, typename T2> using pair = thrust::pair<T1, T2>;
#else
template <typename T1, typename T2> using pair = std::pair<T1, T2>;
#endif

} // namespace detail

template <typename scalar_t, typename index_t>
struct WelfordData {
  scalar_t mean;
  scalar_t m2;
  index_t n;
  scalar_t nf;

  C10_HOST_DEVICE WelfordData() : mean(0), m2(0), n(0), nf(0) {}

  C10_HOST_DEVICE WelfordData(
      scalar_t mean,
      scalar_t m2,
      index_t n,
      scalar_t nf)
      : mean(mean), m2(m2), n(n), nf(nf) {}
};


template <typename scalar_t, typename acc_scalar_t, typename index_t, typename res_t>
struct WelfordOps {
  acc_scalar_t correction;
  bool take_sqrt;
 public:
  using acc_t = WelfordData<acc_scalar_t, index_t>;
  inline C10_DEVICE acc_t reduce(acc_t acc, scalar_t data, index_t /*idx*/) const {
    // We accumulate n in index_t to avoid cumulative rounding error, but still
    // need nf for use in combine where int32 may overflow.
    index_t new_n = acc.n + 1;
    acc_scalar_t new_nf = static_cast<acc_scalar_t>(new_n);
    acc_scalar_t delta = data - acc.mean;
    acc_scalar_t new_mean = acc.mean + delta / new_nf;
    acc_scalar_t new_delta = data - new_mean;
    return {
      new_mean,
      acc.m2 + delta * new_delta,
      new_n,
      new_nf,
    };
  }
  inline C10_DEVICE acc_t combine(acc_t a, acc_t b) const {
    if (a.nf == 0) {
      return b;
    }
    if (b.nf == 0) {
      return a;
    }
    acc_scalar_t delta = b.mean - a.mean;
    acc_scalar_t new_count = a.nf + b.nf;
    acc_scalar_t nb_over_n = b.nf / new_count;
    return {
      a.mean + delta * nb_over_n,
      a.m2 + b.m2 + delta * delta * a.nf * nb_over_n,
      // setting acc.n as -1 since acc.n might not be able to represent the count
      // correctly within its range, setting it to -1 to avoid confusion
      -1,
      new_count
    };
  }
  inline C10_DEVICE res_t project(acc_t acc) const __ubsan_ignore_float_divide_by_zero__ {
    const auto mean = static_cast<scalar_t>(acc.mean);
    const auto divisor = acc.nf > correction ? acc.nf - correction : 0;
    const auto var = acc.m2 / divisor;
    res_t results(take_sqrt ? device_sqrt(var) : var, mean);
    return results;
  }

  static C10_DEVICE acc_t translate_idx(acc_t acc, int64_t /*base_idx*/) {
    return acc;
  }

#if defined(__CUDACC__) || defined(__HIPCC__)
  inline __device__ acc_t warp_shfl_down(acc_t acc, int offset) const {
    return {
      WARP_SHFL_DOWN(acc.mean, offset)
      , WARP_SHFL_DOWN(acc.m2, offset)
      , WARP_SHFL_DOWN(acc.n, offset)
      , WARP_SHFL_DOWN(acc.nf, offset)
    };
  }
#endif
  C10_HOST_DEVICE WelfordOps(acc_scalar_t correction, bool take_sqrt)
      : correction(correction), take_sqrt(take_sqrt) {}
};

template <typename scalar_t, typename acc_t=scalar_t, typename factor_t=acc_t, typename out_t = acc_t>
struct MeanOps {
  factor_t factor;

  inline C10_DEVICE acc_t reduce(acc_t a, scalar_t b, int64_t /*idx*/) const {
    return combine(a, static_cast<acc_t>(b));
  }

  inline C10_DEVICE acc_t combine(acc_t a, acc_t b) const {
    return a + b;
  }

  inline C10_DEVICE out_t project(acc_t a) const {
    return a * factor;
  }

  static C10_DEVICE acc_t translate_idx(acc_t acc, int64_t /*base_idx*/) {
    return acc;
  }

#if defined(__CUDACC__) || defined(__HIPCC__)
  inline C10_DEVICE acc_t warp_shfl_down(acc_t data, int offset) const {
    return WARP_SHFL_DOWN(data, offset);
  }
#endif

  MeanOps(factor_t factor): factor(factor) {
  }
};

// This accumulator template is used to calculate the minimum absolute value of
// a set of numbers.
// `scalar_t` is the type of the input and `acc_t` is the type of the accumulated
// value. These types differ for complex number input support.
template <typename scalar_t, typename acc_t = scalar_t, typename out_t = acc_t>
struct AbsMinOps {

  inline C10_DEVICE acc_t reduce(acc_t acc, scalar_t data, int64_t /*idx*/) const {
    return MIN(acc, static_cast<acc_t>(std::abs(at::opmath_type<scalar_t>(data))));
  }

  inline C10_DEVICE acc_t combine(acc_t a, acc_t b) const {
    return MIN(a, b);
  }

  inline C10_DEVICE out_t project(acc_t a) const {
    return a;
  }

  static C10_DEVICE acc_t translate_idx(acc_t acc, int64_t /*base_idx*/) {
    return acc;
  }

#if defined(__CUDACC__) || defined(__HIPCC__)
  inline C10_DEVICE acc_t warp_shfl_down(acc_t acc, int offset) const {
    return WARP_SHFL_DOWN(acc, offset);
  }
#endif
};

// This accumulator template is used to calculate the maximum absolute value of
// a set of numbers.
// `scalar_t` is the type of the input and `acc_t` is the type of the accumulated
// value. These types differ for complex number input support.
template <typename scalar_t, typename acc_t = scalar_t, typename out_t = acc_t>
struct AbsMaxOps {
  inline C10_DEVICE acc_t reduce(acc_t acc, scalar_t data, int64_t /*idx*/) const {
    return MAX(acc, static_cast<acc_t>(std::abs(at::opmath_type<scalar_t>(data))));
  }

  inline C10_DEVICE acc_t combine(acc_t a, acc_t b) const {
    return MAX(a, b);
  }

  inline C10_DEVICE out_t project(acc_t a) const {
    return a;
  }

  static C10_DEVICE acc_t translate_idx(acc_t acc, int64_t /*base_idx*/) {
    return acc;
  }

#if defined(__CUDACC__) || defined(__HIPCC__)
  inline C10_DEVICE acc_t warp_shfl_down(acc_t acc, int offset) const {
    return WARP_SHFL_DOWN(acc, offset);
  }
#endif
};

// This accumulator template is used to calculate the norm of the absolute value
// of a set of numbers.
// `scalar_t` is the type of the input and `acc_t` is the type of the accumulated
// value. These types differ for complex number input support.
template <typename scalar_t, typename acc_t = scalar_t, typename out_t = acc_t>
struct NormOps {
  acc_t norm_;

  inline C10_DEVICE acc_t reduce(acc_t acc, scalar_t data, int64_t /*idx*/) const {
    return acc + compat_pow(static_cast<acc_t>(std::abs(at::opmath_type<scalar_t>(data))), norm_);
  }

  inline C10_DEVICE acc_t combine(acc_t a, acc_t b) const {
    return a + b;
  }

  inline C10_DEVICE out_t project(acc_t a) const {
    return compat_pow(a, static_cast<acc_t>(1.0) / norm_);
  }

  static C10_DEVICE acc_t translate_idx(acc_t acc, int64_t /*base_idx*/) {
    return acc;
  }

#if defined(__CUDACC__) || defined(__HIPCC__)
  inline C10_DEVICE acc_t warp_shfl_down(acc_t acc, int offset) const {
    return WARP_SHFL_DOWN(acc, offset);
  }
#endif

  NormOps(acc_t norm_): norm_(norm_) {
  }
};

// This accumulator template is used to calculate the order zero norm of the
// absolute value of a set of numbers.
// `scalar_t` is the type of the input and `acc_t` is the type of the accumulated
// value. These types differ for complex number input support.
template <typename scalar_t, typename acc_t = scalar_t, typename out_t = acc_t>
struct NormZeroOps {
  inline C10_DEVICE acc_t reduce(acc_t acc, scalar_t data, int64_t /*idx*/) const {
    return acc + (data == static_cast<scalar_t>(0) ? static_cast<acc_t>(0) : static_cast<acc_t>(1));
  }

  inline C10_DEVICE acc_t combine(acc_t a, acc_t b) const {
    return a + b;
  }

  inline C10_DEVICE out_t project(acc_t a) const {
    return a;
  }

  static C10_DEVICE acc_t translate_idx(acc_t acc, int64_t /*base_idx*/) {
    return acc;
  }


#if defined(__CUDACC__) || defined(__HIPCC__)
  inline C10_DEVICE acc_t warp_shfl_down(acc_t acc, int offset) const {
    return WARP_SHFL_DOWN(acc, offset);
  }
#endif
};

// This accumulator template is used to calculate the order one norm of the
// absolute value of a set of numbers.
// `scalar_t` is the type of the input and `acc_t` is the type of the accumulated
// value. These types differ for complex number input support.
template <typename scalar_t, typename acc_t = scalar_t, typename out_t = acc_t>
struct NormOneOps {
  inline C10_DEVICE acc_t reduce(acc_t acc, scalar_t data, int64_t /*idx*/) const {
    return acc + static_cast<acc_t>(std::abs(at::opmath_type<scalar_t>(data)));
  }

  inline C10_DEVICE acc_t combine(acc_t a, acc_t b) const {
    return a + b;
  }

  inline C10_DEVICE out_t project(acc_t a) const {
    return a;
  }

  static C10_DEVICE acc_t translate_idx(acc_t acc, int64_t /*base_idx*/) {
    return acc;
  }

#if defined(__CUDACC__) || defined(__HIPCC__)
  inline C10_DEVICE acc_t warp_shfl_down(acc_t acc, int offset) const {
    return WARP_SHFL_DOWN(acc, offset);
  }
#endif
};


template<typename acc_t>
struct AbsSwitch {};

template<typename scalar_t, typename acc_t>
inline C10_DEVICE acc_t abs_if_complex(scalar_t data, AbsSwitch<acc_t> /*unused*/) {
  return static_cast<acc_t>(data);
}

template<typename scalar_t, typename acc_t>
inline C10_DEVICE acc_t abs_if_complex(std::complex<scalar_t> data, AbsSwitch<acc_t> /*unused*/) {
  return static_cast<acc_t>(std::abs(data));
}

template<typename scalar_t, typename acc_t>
inline C10_DEVICE acc_t abs_if_complex(c10::complex<scalar_t> data, AbsSwitch<acc_t> /*unused*/) {
  return static_cast<acc_t>(std::abs(at::opmath_type<c10::complex<scalar_t>>(data)));
}

// This accumulator template is used to calculate the order two norm of the
// absolute value of a set of numbers.
// `scalar_t` is the type of the input and `acc_t` is the type of the accumulated
// value. These types differ for complex number input support.
template <typename scalar_t, typename acc_t = scalar_t, typename out_t = acc_t>
struct NormTwoOps {
  inline C10_DEVICE acc_t reduce(acc_t acc, scalar_t data, int64_t /*idx*/) const {
    acc_t data_ = abs_if_complex(data, AbsSwitch<acc_t>());
    return acc + data_ * data_;
  }

  inline C10_DEVICE acc_t combine(acc_t a, acc_t b) const {
    return a + b;
  }

  inline C10_DEVICE out_t project(acc_t a) const {
    return device_sqrt(a);
  }

  static C10_DEVICE acc_t translate_idx(acc_t acc, int64_t /*base_idx*/) {
    return acc;
  }

#if defined(__CUDACC__) || defined(__HIPCC__)
  inline C10_DEVICE acc_t warp_shfl_down(acc_t acc, int offset) const {
    return WARP_SHFL_DOWN(acc, offset);
  }
#endif
};

template <typename acc_t, typename data_t>
struct NanSumOps {
  inline C10_DEVICE acc_t reduce(acc_t a, data_t b, int64_t /*idx*/) const {
    return a + (at::_isnan(b) ? acc_t{0.} : acc_t{b});
  }

  inline C10_DEVICE acc_t combine(acc_t a, acc_t b) const {
    return  a + b;
  }

  inline C10_DEVICE data_t project(acc_t a) const {
    return data_t{a};
  }

  static C10_DEVICE acc_t translate_idx(acc_t acc, int64_t /*base_idx*/) {
    return acc;
  }

#if defined(__CUDACC__) || defined(__HIPCC__)
  inline C10_DEVICE acc_t warp_shfl_down(acc_t data, int offset) const {
    return WARP_SHFL_DOWN(data, offset);
  }
#endif
};

namespace detail {

template <typename scalar_t>
struct LessOrNan {
  C10_DEVICE bool operator () (scalar_t a, scalar_t b, int64_t idx_a, int64_t idx_b) const {
    // If (a == b), then choose the one with lower idx, else min(a, b)
    if (at::_isnan(a)) {
      if (at::_isnan(b)) {
        return idx_a < idx_b;
      }
      return true;
    }
    return (a == b) ? idx_a < idx_b : (a < b);
  }
};

template <typename scalar_t>
struct GreaterOrNan {
  C10_DEVICE bool operator () (scalar_t a, scalar_t b, int64_t idx_a, int64_t idx_b) const {
    // If (a == b), then choose the one with lower idx, else max(a, b)
    if (at::_isnan(a)) {
      if (at::_isnan(b)) {
        return idx_a < idx_b;
      }
      return true;
    }
    return (a == b) ? idx_a < idx_b : (a > b);
  }
};

template <typename comp_t>
struct MinMaxReductionOps {
  using scalar_t = typename binary_function_traits<comp_t>::arg1_t;
  using index_t = int64_t;
  using arg_t = detail::pair<scalar_t, index_t>;

  static C10_DEVICE arg_t project(arg_t arg) {
    return arg;
  }

  static C10_DEVICE arg_t reduce(arg_t arg, scalar_t val, int64_t idx) {
    return comp_t{}(arg.first, val, arg.second, idx) ? arg : arg_t(val, idx);
  }

  static C10_DEVICE arg_t combine(arg_t a, arg_t b) {
    return comp_t{}(a.first, b.first, a.second, b.second) ? a : b;
  }

  static C10_DEVICE arg_t translate_idx(arg_t a, int64_t base_idx) {
    return {a.first, a.second + base_idx};
  }

#if defined(__CUDACC__) || defined(__HIPCC__)
  static C10_DEVICE arg_t warp_shfl_down(arg_t arg, int offset) {
    return arg_t(WARP_SHFL_DOWN(arg.first, offset),
                 WARP_SHFL_DOWN(arg.second, offset));
  }
#endif
};

template <typename comp_t>
struct ArgReductionOps : public MinMaxReductionOps<comp_t> {
  using typename MinMaxReductionOps<comp_t>::scalar_t;
  using typename MinMaxReductionOps<comp_t>::index_t;
  using typename MinMaxReductionOps<comp_t>::arg_t;

  static C10_DEVICE index_t project(arg_t arg) {
    return arg.second;
  }
};

} // namespace detail

template <typename scalar_t>
struct ArgMaxOps :
  public detail::ArgReductionOps<detail::GreaterOrNan<scalar_t>> {
};

template <typename scalar_t>
struct ArgMinOps :
  public detail::ArgReductionOps<detail::LessOrNan<scalar_t>> {
};

template <typename scalar_t>
struct MinOps :
  public detail::MinMaxReductionOps<detail::LessOrNan<scalar_t>> {
};

template <typename scalar_t>
struct MaxOps :
  public detail::MinMaxReductionOps<detail::GreaterOrNan<scalar_t>> {
};

template <typename scalar_t, typename acc_scalar_t, typename index_t>
struct MinMaxOps {
  using acc_t = detail::pair<acc_scalar_t, acc_scalar_t>;
  inline C10_DEVICE acc_t reduce(acc_t acc, scalar_t data, index_t /*idx*/) const {
    return combine(acc, {data, data});
  }

  inline C10_DEVICE acc_t combine(acc_t a, acc_t b) const {
    auto min_val = (at::_isnan(a.first) || a.first < b.first) ? a.first : b.first;
    auto max_val = (at::_isnan(a.second) || a.second > b.second) ? a.second : b.second;

    return {min_val, max_val};
  }

  inline C10_DEVICE acc_t project(acc_t acc) const {
    return acc;
  }

  static C10_DEVICE acc_t translate_idx(acc_t acc, int64_t /*base_idx*/) {
    return acc;
  }

#if defined(__CUDACC__) || defined(__HIPCC__)
  inline C10_DEVICE acc_t warp_shfl_down(acc_t acc, int offset) const {
    return {
      WARP_SHFL_DOWN(acc.first, offset), WARP_SHFL_DOWN(acc.second, offset)
    };
  }
#endif
};

} // namespace at::native

#undef MAX
#undef MIN

#else
#error "This file should not be included when either TORCH_STABLE_ONLY or TORCH_TARGET_VERSION is defined."
#endif  // !defined(TORCH_STABLE_ONLY) && !defined(TORCH_TARGET_VERSION)
