#pragma once

// DO NOT DEFINE STATIC DATA IN THIS HEADER!
// See Note [Do not compile initializers with AVX]

#include <ATen/cpu/vec/intrinsics.h>
#include <ATen/cpu/vec/vec_base.h>
#include <c10/util/irange.h>
#if defined(CPU_CAPABILITY_AVX2)
#define SLEEF_STATIC_LIBS
#include <sleef.h>
#endif

namespace at::vec {
// See Note [CPU_CAPABILITY namespace]
inline namespace CPU_CAPABILITY {

#if defined(CPU_CAPABILITY_AVX2)

template <>
struct is_vec_specialized_for<float> : std::bool_constant<true> {};

template <>
class Vectorized<float> {
 private:
  __m256 values;

 public:
  using value_type = float;
  using size_type = int;
  static constexpr size_type size() {
    return 8;
  }
  Vectorized() {}
  Vectorized(__m256 v) : values(v) {}
  Vectorized(float val) {
    values = _mm256_set1_ps(val);
  }
  Vectorized(
      float val1,
      float val2,
      float val3,
      float val4,
      float val5,
      float val6,
      float val7,
      float val8) {
    values = _mm256_setr_ps(val1, val2, val3, val4, val5, val6, val7, val8);
  }
  Vectorized(const float (&arr)[8])
      : Vectorized(
            arr[0],
            arr[1],
            arr[2],
            arr[3],
            arr[4],
            arr[5],
            arr[6],
            arr[7]) {}
  operator __m256() const {
    return values;
  }
  template <int64_t mask>
  static Vectorized<float> blend(
      const Vectorized<float>& a,
      const Vectorized<float>& b) {
    return _mm256_blend_ps(a.values, b.values, mask);
  }
  static Vectorized<float> blendv(
      const Vectorized<float>& a,
      const Vectorized<float>& b,
      const Vectorized<float>& mask) {
    return _mm256_blendv_ps(a.values, b.values, mask.values);
  }
  template <typename step_t>
  static Vectorized<float> arange(
      float base = 0.f,
      step_t step = static_cast<step_t>(1)) {
    return Vectorized<float>(
        base,
        base + step,
        base + 2 * step,
        base + 3 * step,
        base + 4 * step,
        base + 5 * step,
        base + 6 * step,
        base + 7 * step);
  }
  static Vectorized<float> set(
      const Vectorized<float>& a,
      const Vectorized<float>& b,
      int64_t count = size()) {
    switch (count) {
      case 0:
        return a;
      case 1:
        return blend<1>(a, b);
      case 2:
        return blend<3>(a, b);
      case 3:
        return blend<7>(a, b);
      case 4:
        return blend<15>(a, b);
      case 5:
        return blend<31>(a, b);
      case 6:
        return blend<63>(a, b);
      case 7:
        return blend<127>(a, b);
    }
    return b;
  }
  static Vectorized<float> loadu(const void* ptr, int64_t count = size()) {
    if (count == size())
      return _mm256_loadu_ps(reinterpret_cast<const float*>(ptr));
    __at_align__ float tmp_values[size()];
    // Ensure uninitialized memory does not change the output value See
    // https://github.com/pytorch/pytorch/issues/32502 for more details. We do
    // not initialize arrays to zero using "={0}" because gcc would compile it
    // to two instructions while a loop would be compiled to one instruction.
    for (const auto i : c10::irange(size())) {
      tmp_values[i] = 0.0;
    }
    std::memcpy(
        tmp_values, reinterpret_cast<const float*>(ptr), count * sizeof(float));
    return _mm256_loadu_ps(tmp_values);
  }
  void store(void* ptr, int64_t count = size()) const {
    if (count == size()) {
      _mm256_storeu_ps(reinterpret_cast<float*>(ptr), values);
    } else if (count > 0) {
      float tmp_values[size()];
      _mm256_storeu_ps(reinterpret_cast<float*>(tmp_values), values);
      std::memcpy(ptr, tmp_values, count * sizeof(float));
    }
  }
  const float& operator[](int idx) const = delete;
  float& operator[](int idx) = delete;
  int zero_mask() const {
    // returns an integer mask where all zero elements are translated to 1-bit
    // and others are translated to 0-bit
    __m256 cmp = _mm256_cmp_ps(values, _mm256_set1_ps(0.0f), _CMP_EQ_OQ);
    return _mm256_movemask_ps(cmp);
  }
  Vectorized<float> isnan() const {
    return _mm256_cmp_ps(values, _mm256_set1_ps(0.0f), _CMP_UNORD_Q);
  }

  bool has_inf_nan() const {
    __m256 self_sub = _mm256_sub_ps(values, values);
    return (_mm256_movemask_epi8(_mm256_castps_si256(self_sub)) & 0x77777777) !=
        0;
  }

  Vectorized<float> map(float (*const f)(float)) const {
    __at_align__ float tmp[size()];
    store(tmp);
    for (const auto i : c10::irange(size())) {
      tmp[i] = f(tmp[i]);
    }
    return loadu(tmp);
  }
  Vectorized<float> abs() const {
    auto mask = _mm256_set1_ps(-0.f);
    return _mm256_andnot_ps(mask, values);
  }
  Vectorized<float> angle() const {
    const auto zero_vec = _mm256_set1_ps(0.f);
    const auto nan_vec = _mm256_set1_ps(NAN);
    const auto not_nan_mask = _mm256_cmp_ps(values, values, _CMP_EQ_OQ);
    const auto nan_mask = _mm256_cmp_ps(not_nan_mask, zero_vec, _CMP_EQ_OQ);
    const auto pi = _mm256_set1_ps(c10::pi<float>);

    const auto neg_mask = _mm256_cmp_ps(values, zero_vec, _CMP_LT_OQ);
    auto angle = _mm256_blendv_ps(zero_vec, pi, neg_mask);
    angle = _mm256_blendv_ps(angle, nan_vec, nan_mask);
    return angle;
  }
  Vectorized<float> real() const {
    return *this;
  }
  Vectorized<float> imag() const {
    return _mm256_set1_ps(0);
  }
  Vectorized<float> conj() const {
    return *this;
  }
  Vectorized<float> acos() const {
    return Vectorized<float>(Sleef_acosf8_u10(values));
  }
  Vectorized<float> acosh() const {
    return Vectorized<float>(Sleef_acoshf8_u10(values));
  }
  Vectorized<float> asin() const {
    return Vectorized<float>(Sleef_asinf8_u10(values));
  }
  Vectorized<float> asinh() const {
    return Vectorized<float>(Sleef_asinhf8_u10(values));
  }
  Vectorized<float> atan() const {
    return Vectorized<float>(Sleef_atanf8_u10(values));
  }
  Vectorized<float> atanh() const {
    return Vectorized<float>(Sleef_atanhf8_u10(values));
  }
  Vectorized<float> atan2(const Vectorized<float>& b) const {
    return Vectorized<float>(Sleef_atan2f8_u10(values, b));
  }
  Vectorized<float> copysign(const Vectorized<float>& sign) const {
    return Vectorized<float>(Sleef_copysignf8(values, sign));
  }
  Vectorized<float> erf() const {
    // constants
    const auto neg_zero_vec = _mm256_set1_ps(-0.f);
    const auto one_vec = _mm256_set1_ps(1.0f);
    const auto p = _mm256_set1_ps(0.3275911f);
    const auto p1 = _mm256_set1_ps(0.254829592f);
    const auto p2 = _mm256_set1_ps(-0.284496736f);
    const auto p3 = _mm256_set1_ps(1.421413741f);
    const auto p4 = _mm256_set1_ps(-1.453152027f);
    const auto p5 = _mm256_set1_ps(1.061405429f);
    // sign(x)
    auto sign_mask = _mm256_and_ps(neg_zero_vec, values);
    auto abs_vec = _mm256_xor_ps(sign_mask, values);
    // t = 1 / (p * abs(x) + 1)
    auto tmp0 = _mm256_fmadd_ps(p, abs_vec, one_vec);
    auto t = _mm256_div_ps(one_vec, tmp0);
    // r = p5 * t ^ 4 + p4 * t ^ 3 + p3 * t ^ 2 + p2 * t + p1
    auto tmp1 = _mm256_fmadd_ps(p5, t, p4);
    auto tmp2 = _mm256_fmadd_ps(tmp1, t, p3);
    auto tmp3 = _mm256_fmadd_ps(tmp2, t, p2);
    auto r = _mm256_fmadd_ps(tmp3, t, p1);
    // - exp(- x * x)
    auto pow_2 = _mm256_mul_ps(values, values);
    auto neg_pow_2 = _mm256_xor_ps(neg_zero_vec, pow_2);
    // auto tmp4 = exp(neg_pow_2);
    auto tmp4 = Vectorized<float>(Sleef_expf8_u10(neg_pow_2));
    auto tmp5 = _mm256_xor_ps(neg_zero_vec, tmp4);
    // erf(x) = sign(x) * (1 - r * t * exp(- x * x))
    auto tmp6 = _mm256_mul_ps(tmp5, t);
    auto tmp7 = _mm256_fmadd_ps(tmp6, r, one_vec);
    return _mm256_xor_ps(sign_mask, tmp7);
  }
  Vectorized<float> erfc() const {
    return Vectorized<float>(Sleef_erfcf8_u15(values));
  }
  Vectorized<float> erfinv() const {
    return map(calc_erfinv);
  }
  Vectorized<float> exp() const {
    return Vectorized<float>(Sleef_expf8_u10(values));
  }
  Vectorized<float> exp2() const {
    return Vectorized<float>(Sleef_exp2f8_u10(values));
  }
  Vectorized<float> expm1() const {
    return Vectorized<float>(Sleef_expm1f8_u10(values));
  }
  Vectorized<float> exp_u20() const {
    // A faster version of exp with ULP=20
    const __m256 vec_factorial_1 =
        _mm256_set1_ps(0.999999701f); // 1/factorial(1)
    const __m256 vec_factorial_2 =
        _mm256_set1_ps(0.499991506f); // 1/factorial(2)
    const __m256 vec_factorial_3 =
        _mm256_set1_ps(0.166676521f); // 1/factorial(3)
    const __m256 vec_factorial_4 =
        _mm256_set1_ps(0.0418978221f); // 1/factorial(4)
    const __m256 vec_factorial_5 =
        _mm256_set1_ps(0.00828929059f); // 1/factorial(5)
    const __m256 vec_exp_log2ef =
        _mm256_castsi256_ps(_mm256_set1_epi32(0x3fb8aa3b)); // log2(e)
    const __m256 vec_half = _mm256_set1_ps(0.5f);
    const __m256 vec_one = _mm256_set1_ps(1.f);
    const __m256 vec_zero = _mm256_set1_ps(0.f);
    const __m256 vec_two = _mm256_set1_ps(2.f);
    const __m256 vec_ln2f =
        _mm256_castsi256_ps(_mm256_set1_epi32(0x3f317218)); // ln(2)
    const __m256 vec_ln_flt_min =
        _mm256_castsi256_ps(_mm256_set1_epi32(0xc2aeac50));
    const __m256 vec_ln_flt_max =
        _mm256_castsi256_ps(_mm256_set1_epi32(0x42b17218));
    const __m256i vec_127 = _mm256_set1_epi32(0x0000007f);
    const int n_mantissa_bits = 23;

    // exp(x) =
    // = exp(n * ln(2) + r) // divide x by ln(2) and get quot and rem
    // = 2^n * exp(r) // simplify the exp(n*ln(2)) expression

    auto less_ln_flt_min_mask =
        _mm256_cmp_ps(values, vec_ln_flt_min, 1 /*_CMP_LT_OS*/);
    auto vec_src = _mm256_min_ps(values, vec_ln_flt_max);
    vec_src = _mm256_max_ps(vec_src, vec_ln_flt_min);

    // fx = floorf(x * log2ef + 0.5)
    auto vec_fx = _mm256_fmadd_ps(vec_src, vec_exp_log2ef, vec_half);
    vec_fx = _mm256_floor_ps(vec_fx);

    // x = x - fx * ln2
    auto vec_exp_poly = _mm256_fnmadd_ps(vec_fx, vec_ln2f, vec_src);

    // compute polynomial
    auto vec_res =
        _mm256_fmadd_ps(vec_exp_poly, vec_factorial_5, vec_factorial_4);
    vec_res = _mm256_fmadd_ps(vec_exp_poly, vec_res, vec_factorial_3);
    vec_res = _mm256_fmadd_ps(vec_exp_poly, vec_res, vec_factorial_2);
    vec_res = _mm256_fmadd_ps(vec_exp_poly, vec_res, vec_factorial_1);
    vec_res = _mm256_fmadd_ps(vec_exp_poly, vec_res, vec_one);

    // compute 2^(n-1)
    auto vec_exp_number = _mm256_sub_ps(vec_fx, vec_one);
    auto vec_exp_number_i = _mm256_cvtps_epi32(vec_exp_number);
    auto vec_two_pow_n_i = _mm256_add_epi32(vec_exp_number_i, vec_127);
    vec_two_pow_n_i = _mm256_slli_epi32(vec_two_pow_n_i, n_mantissa_bits);
    auto vec_two_pow_n = _mm256_castsi256_ps(vec_two_pow_n_i);
    vec_two_pow_n =
        _mm256_blendv_ps(vec_two_pow_n, vec_zero, less_ln_flt_min_mask);

    // y = y * 2^n
    vec_res = _mm256_mul_ps(vec_res, vec_two_pow_n);
    vec_res = _mm256_mul_ps(vec_res, vec_two);
    return vec_res;
  }
  Vectorized<float> fmod(const Vectorized<float>& q) const {
    return Vectorized<float>(Sleef_fmodf8(values, q));
  }
  Vectorized<float> log() const {
    return Vectorized<float>(Sleef_logf8_u10(values));
  }
  Vectorized<float> log2() const {
    return Vectorized<float>(Sleef_log2f8_u10(values));
  }
  Vectorized<float> log10() const {
    return Vectorized<float>(Sleef_log10f8_u10(values));
  }
  Vectorized<float> log1p() const {
    return Vectorized<float>(Sleef_log1pf8_u10(values));
  }
  Vectorized<float> frac() const;
  Vectorized<float> sin() const {
    return Vectorized<float>(Sleef_sinf8_u35(values));
  }
  Vectorized<float> sinh() const {
    return Vectorized<float>(Sleef_sinhf8_u10(values));
  }
  Vectorized<float> cos() const {
    return Vectorized<float>(Sleef_cosf8_u35(values));
  }
  Vectorized<float> cosh() const {
    return Vectorized<float>(Sleef_coshf8_u10(values));
  }
  Vectorized<float> ceil() const {
    return _mm256_ceil_ps(values);
  }
  Vectorized<float> floor() const {
    return _mm256_floor_ps(values);
  }
  Vectorized<float> hypot(const Vectorized<float>& b) const {
    return Vectorized<float>(Sleef_hypotf8_u05(values, b));
  }
  Vectorized<float> i0() const {
    return map(calc_i0);
  }
  Vectorized<float> i0e() const {
    return map(calc_i0e);
  }
  Vectorized<float> digamma() const {
    return map(calc_digamma);
  }
  Vectorized<float> igamma(const Vectorized<float>& x) const {
    __at_align__ float tmp[size()];
    __at_align__ float tmp_x[size()];
    store(tmp);
    x.store(tmp_x);
    for (const auto i : c10::irange(size())) {
      tmp[i] = calc_igamma(tmp[i], tmp_x[i]);
    }
    return loadu(tmp);
  }
  Vectorized<float> igammac(const Vectorized<float>& x) const {
    __at_align__ float tmp[size()];
    __at_align__ float tmp_x[size()];
    store(tmp);
    x.store(tmp_x);
    for (const auto i : c10::irange(size())) {
      tmp[i] = calc_igammac(tmp[i], tmp_x[i]);
    }
    return loadu(tmp);
  }
  Vectorized<float> neg() const {
    return _mm256_xor_ps(_mm256_set1_ps(-0.f), values);
  }
  Vectorized<float> nextafter(const Vectorized<float>& b) const {
    return Vectorized<float>(Sleef_nextafterf8(values, b));
  }
  Vectorized<float> round() const {
    return _mm256_round_ps(
        values, (_MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC));
  }
  Vectorized<float> tan() const {
    return Vectorized<float>(Sleef_tanf8_u10(values));
  }
  Vectorized<float> tanh() const {
    return Vectorized<float>(Sleef_tanhf8_u10(values));
  }
  Vectorized<float> trunc() const {
    return _mm256_round_ps(values, (_MM_FROUND_TO_ZERO | _MM_FROUND_NO_EXC));
  }
  Vectorized<float> lgamma() const {
    return Vectorized<float>(Sleef_lgammaf8_u10(values));
  }
  Vectorized<float> sqrt() const {
    return _mm256_sqrt_ps(values);
  }
  Vectorized<float> reciprocal() const {
    return _mm256_div_ps(_mm256_set1_ps(1), values);
  }
  Vectorized<float> rsqrt() const {
    return _mm256_div_ps(_mm256_set1_ps(1), _mm256_sqrt_ps(values));
  }
  Vectorized<float> pow(const Vectorized<float>& b) const {
    return Vectorized<float>(Sleef_powf8_u10(values, b));
  }
  float reduce_add() const {
    auto v = values;
    // 128-bit shuffle
    auto v1 = _mm256_permute2f128_ps(v, v, 0x1);
    v = _mm256_add_ps(v, v1);
    // 64-bit shuffle
    v1 = _mm256_shuffle_ps(v, v, 0x4E);
    v = _mm256_add_ps(v, v1);
    // 32-bit shuffle
    v1 = _mm256_shuffle_ps(v, v, 0xB1);
    v = _mm256_add_ps(v, v1);
    return _mm256_cvtss_f32(v);
  }
  float reduce_max() const {
    auto v = values;
    // 128-bit shuffle
    auto v1 = _mm256_permute2f128_ps(v, v, 0x1);
    v = _mm256_max_ps(v, v1);
    // 64-bit shuffle
    v1 = _mm256_shuffle_ps(v, v, 0x4E);
    v = _mm256_max_ps(v, v1);
    // 32-bit shuffle
    v1 = _mm256_shuffle_ps(v, v, 0xB1);
    v = _mm256_max_ps(v, v1);
    return _mm256_cvtss_f32(v);
  }
  // Comparison using the _CMP_**_OQ predicate.
  //   `O`: get false if an operand is NaN
  //   `Q`: do not raise if an operand is NaN
  Vectorized<float> operator==(const Vectorized<float>& other) const {
    return _mm256_cmp_ps(values, other.values, _CMP_EQ_OQ);
  }

  Vectorized<float> operator!=(const Vectorized<float>& other) const {
    return _mm256_cmp_ps(values, other.values, _CMP_NEQ_UQ);
  }

  Vectorized<float> operator<(const Vectorized<float>& other) const {
    return _mm256_cmp_ps(values, other.values, _CMP_LT_OQ);
  }

  Vectorized<float> operator<=(const Vectorized<float>& other) const {
    return _mm256_cmp_ps(values, other.values, _CMP_LE_OQ);
  }

  Vectorized<float> operator>(const Vectorized<float>& other) const {
    return _mm256_cmp_ps(values, other.values, _CMP_GT_OQ);
  }

  Vectorized<float> operator>=(const Vectorized<float>& other) const {
    return _mm256_cmp_ps(values, other.values, _CMP_GE_OQ);
  }

  Vectorized<float> eq(const Vectorized<float>& other) const;
  Vectorized<float> ne(const Vectorized<float>& other) const;
  Vectorized<float> gt(const Vectorized<float>& other) const;
  Vectorized<float> ge(const Vectorized<float>& other) const;
  Vectorized<float> lt(const Vectorized<float>& other) const;
  Vectorized<float> le(const Vectorized<float>& other) const;
};

template <>
Vectorized<float> inline operator+(
    const Vectorized<float>& a,
    const Vectorized<float>& b) {
  return _mm256_add_ps(a, b);
}

template <>
Vectorized<float> inline operator-(
    const Vectorized<float>& a,
    const Vectorized<float>& b) {
  return _mm256_sub_ps(a, b);
}

template <>
Vectorized<float> inline operator*(
    const Vectorized<float>& a,
    const Vectorized<float>& b) {
  return _mm256_mul_ps(a, b);
}

template <>
Vectorized<float> inline operator/(
    const Vectorized<float>& a,
    const Vectorized<float>& b) {
  return _mm256_div_ps(a, b);
}

// frac. Implement this here so we can use subtraction
inline Vectorized<float> Vectorized<float>::frac() const {
  return *this - this->trunc();
}

// Implements the IEEE 754 201X `maximum` operation, which propagates NaN if
// either input is a NaN.
template <>
Vectorized<float> inline maximum(
    const Vectorized<float>& a,
    const Vectorized<float>& b) {
  Vectorized<float> max = _mm256_max_ps(a, b);
  Vectorized<float> isnan = _mm256_cmp_ps(a, b, _CMP_UNORD_Q);
  // Exploit the fact that all-ones is a NaN.
  return _mm256_or_ps(max, isnan);
}

// Implements the IEEE 754 201X `minimum` operation, which propagates NaN if
// either input is a NaN.
template <>
Vectorized<float> inline minimum(
    const Vectorized<float>& a,
    const Vectorized<float>& b) {
  Vectorized<float> min = _mm256_min_ps(a, b);
  Vectorized<float> isnan = _mm256_cmp_ps(a, b, _CMP_UNORD_Q);
  // Exploit the fact that all-ones is a NaN.
  return _mm256_or_ps(min, isnan);
}

template <>
Vectorized<float> inline clamp(
    const Vectorized<float>& a,
    const Vectorized<float>& min,
    const Vectorized<float>& max) {
  return _mm256_min_ps(max, _mm256_max_ps(min, a));
}

template <>
Vectorized<float> inline clamp_max(
    const Vectorized<float>& a,
    const Vectorized<float>& max) {
  return _mm256_min_ps(max, a);
}

template <>
Vectorized<float> inline clamp_min(
    const Vectorized<float>& a,
    const Vectorized<float>& min) {
  return _mm256_max_ps(min, a);
}

template <>
Vectorized<float> inline operator&(
    const Vectorized<float>& a,
    const Vectorized<float>& b) {
  return _mm256_and_ps(a, b);
}

template <>
Vectorized<float> inline operator|(
    const Vectorized<float>& a,
    const Vectorized<float>& b) {
  return _mm256_or_ps(a, b);
}

template <>
Vectorized<float> inline operator^(
    const Vectorized<float>& a,
    const Vectorized<float>& b) {
  return _mm256_xor_ps(a, b);
}

inline Vectorized<float> Vectorized<float>::eq(
    const Vectorized<float>& other) const {
  return (*this == other) & Vectorized<float>(1.0f);
}

inline Vectorized<float> Vectorized<float>::ne(
    const Vectorized<float>& other) const {
  return (*this != other) & Vectorized<float>(1.0f);
}

inline Vectorized<float> Vectorized<float>::gt(
    const Vectorized<float>& other) const {
  return (*this > other) & Vectorized<float>(1.0f);
}

inline Vectorized<float> Vectorized<float>::ge(
    const Vectorized<float>& other) const {
  return (*this >= other) & Vectorized<float>(1.0f);
}

inline Vectorized<float> Vectorized<float>::lt(
    const Vectorized<float>& other) const {
  return (*this < other) & Vectorized<float>(1.0f);
}

inline Vectorized<float> Vectorized<float>::le(
    const Vectorized<float>& other) const {
  return (*this <= other) & Vectorized<float>(1.0f);
}

template <>
inline void convert(const float* src, float* dst, int64_t n) {
  int64_t i;
#ifndef __msvc_cl__
#pragma unroll
#endif
  for (i = 0; i <= (n - Vectorized<float>::size());
       i += Vectorized<float>::size()) {
    _mm256_storeu_ps(dst + i, _mm256_loadu_ps(src + i));
  }
#ifndef __msvc_cl__
#pragma unroll
#endif
  for (; i < n; i++) {
    dst[i] = src[i];
  }
}

template <>
Vectorized<float> inline fmadd(
    const Vectorized<float>& a,
    const Vectorized<float>& b,
    const Vectorized<float>& c) {
  return _mm256_fmadd_ps(a, b, c);
}

template <>
Vectorized<float> inline fmsub(
    const Vectorized<float>& a,
    const Vectorized<float>& b,
    const Vectorized<float>& c) {
  return _mm256_fmsub_ps(a, b, c);
}

// TODO: rewrite with ATEN vectorized (need to add unpack and shuffle)
// Used by Inductor CPP codegen for micro gemm
inline void transpose_block(at::vec::VectorizedN<float, 8>& input) {
  __m256 temp0[8];
  // unpacking and interleaving 32-bit elements
  // a0  b0  a1  b1  a4  b4  a5  b5
  // a2  b2  a3  b3  a6  b6  a7  b7
  // c0  d0  c1  d1 ...
  // c2  d2  c3  d3 ...
  // e0  f0  e1  f1 ...
  // e2  f2  e3  f3 ...
  // g0  h0  g1  h1 ...
  // g2  h2  g3  h3 ...
  temp0[0] = _mm256_unpacklo_ps(input[0], input[1]);
  temp0[1] = _mm256_unpackhi_ps(input[0], input[1]);
  temp0[2] = _mm256_unpacklo_ps(input[2], input[3]);
  temp0[3] = _mm256_unpackhi_ps(input[2], input[3]);
  temp0[4] = _mm256_unpacklo_ps(input[4], input[5]);
  temp0[5] = _mm256_unpackhi_ps(input[4], input[5]);
  temp0[6] = _mm256_unpacklo_ps(input[6], input[7]);
  temp0[7] = _mm256_unpackhi_ps(input[6], input[7]);

  __m256 temp1[8];
  // unpacking and interleaving 64-bit elements
  //  a0  b0  c0  d0  a4  b4  c4  d4
  //  a1  b1  c1  d1 ...
  //  a2  b2  c2  d2 ...
  //  a3  b3  c3  d3 ...
  //  e0  f0  g0  h0  e4  f4  g4  h4
  //  e1  f1  g1  h1 ...
  //  e2  f2  g2  h2 ...
  //  e3  f3  g3  h3 ...
  temp1[0] = _mm256_castpd_ps(_mm256_unpacklo_pd(
      _mm256_castps_pd(temp0[0]), _mm256_castps_pd(temp0[2])));
  temp1[1] = _mm256_castpd_ps(_mm256_unpackhi_pd(
      _mm256_castps_pd(temp0[0]), _mm256_castps_pd(temp0[2])));
  temp1[2] = _mm256_castpd_ps(_mm256_unpacklo_pd(
      _mm256_castps_pd(temp0[1]), _mm256_castps_pd(temp0[3])));
  temp1[3] = _mm256_castpd_ps(_mm256_unpackhi_pd(
      _mm256_castps_pd(temp0[1]), _mm256_castps_pd(temp0[3])));
  temp1[4] = _mm256_castpd_ps(_mm256_unpacklo_pd(
      _mm256_castps_pd(temp0[4]), _mm256_castps_pd(temp0[6])));
  temp1[5] = _mm256_castpd_ps(_mm256_unpackhi_pd(
      _mm256_castps_pd(temp0[4]), _mm256_castps_pd(temp0[6])));
  temp1[6] = _mm256_castpd_ps(_mm256_unpacklo_pd(
      _mm256_castps_pd(temp0[5]), _mm256_castps_pd(temp0[7])));
  temp1[7] = _mm256_castpd_ps(_mm256_unpackhi_pd(
      _mm256_castps_pd(temp0[5]), _mm256_castps_pd(temp0[7])));

  //  shuffle 128-bits (composed of 4 32-bit elements)
  //  a0  b0  c0  d0  e0  f0  g0  h0
  //  a1  b1  c1  d1 ...
  //  a2  b2  c2  d2 ...
  //  a3  b3  c3  d3 ...
  //  a4  b4  c4  d4 ...
  //  a5  b5  c5  d5 ...
  //  a6  b6  c6  d6 ...
  //  a7  b7  c7  d7 ...
  input[0] = _mm256_permute2f128_ps(temp1[0], temp1[4], 0x20);
  input[1] = _mm256_permute2f128_ps(temp1[1], temp1[5], 0x20);
  input[2] = _mm256_permute2f128_ps(temp1[2], temp1[6], 0x20);
  input[3] = _mm256_permute2f128_ps(temp1[3], temp1[7], 0x20);
  input[4] = _mm256_permute2f128_ps(temp1[0], temp1[4], 0x31);
  input[5] = _mm256_permute2f128_ps(temp1[1], temp1[5], 0x31);
  input[6] = _mm256_permute2f128_ps(temp1[2], temp1[6], 0x31);
  input[7] = _mm256_permute2f128_ps(temp1[3], temp1[7], 0x31);
}

// Used by Inductor CPP codegen
template <>
inline void transpose_mxn<float, 8, 8>(
    const float* src,
    int64_t ld_src,
    float* dst,
    int64_t ld_dst) {
  // load from src to registers
  at::vec::VectorizedN<float, 8> input;
  // a: a0  a1  a2  a3  a4  a5  a6  a7
  // b: b0  b1  b2  b3  b4  b5  b6  b7
  // c: c0  c1  c2  c3  c4  c5  c6  c7
  // d: d0  d1  d2  d3  d4  d5  d6  d7
  // e: e0  e1  e2  e3  e4  e5  e6  e7
  // f: f0  f1  f2  f3  f4  f5  f6  f7
  // g: g0  g1  g2  g3  g4  g5  g6  g7
  // h: h0  h1  h2  h3  h4  h5  h6  h7
  int i;
#ifndef __msvc_cl__
#pragma unroll
#endif
  for (i = 0; i < 8; i++) {
    input[i] = _mm256_loadu_ps(&src[i * ld_src]);
  }

  transpose_block(input);

  // store from registers to dst
#ifndef __msvc_cl__
#pragma unroll
#endif
  for (i = 0; i < 8; i++) {
    _mm256_storeu_ps(&dst[i * ld_dst], input[i]);
  }
}

template <>
inline void transpose_mxn<float, 16, 16>(
    const float* src,
    int64_t ld_src,
    float* dst,
    int64_t ld_dst) {
  transpose_mxn<float, 8, 8>(src, ld_src, dst, ld_dst);
  transpose_mxn<float, 8, 8>(src + 8, ld_src, dst + 8 * ld_dst, ld_dst);
  transpose_mxn<float, 8, 8>(src + 8 * ld_src, ld_src, dst + 8, ld_dst);
  transpose_mxn<float, 8, 8>(
      src + 8 * ld_src + 8, ld_src, dst + 8 * ld_dst + 8, ld_dst);
}
#endif

} // namespace CPU_CAPABILITY
} // namespace at::vec